chemical techniques

Chemical Analysis

Second Edition

Chemical AnalysisModern Instrumentation Methods and Techniques

Second Edition

Francis Rouessac and Annick RouessacUniversity of Le Mans, France

Translated byFrancis and Annick Rouessac and Steve Brooks

English language translation copyright © 2007 by John Wiley & Sons Ltd,The Atrium, Southern Gate, Chichester,West Sussex PO19 8SQ, England

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Translated into English by Francis and Annick Rouessac and Steve Brooks

First Published in French © 1992 Masson2nd Edition © 1994 Masson3rd Edition © 1997 Masson4th Edition © 1998 Dunod5th Edition © 2000 Dunod6th Edition © 2004 Dunod

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Rouessac, Francis.[Analyse chimique. English]Chemical analysis : modern instrumentation and methods and techniques / Francis Rouessac and AnnickRouessac ; translated by Steve Brooks and Francis and Annick Rouessac. — 2nd ed.

p. cm.Includes bibliographical references and index.ISBN 978-0-470-85902-5 (cloth : alk. paper) — ISBN 978-0-470-85903-2 (pbk. : alk. paper)1. Instrumental analysis. I. Rouessac, Annick. II. Title.QD79.I5R6813 2007543—dc22 2006036196

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

ISBN 978-0-470-85902-5 (HB)ISBN 978-0-470-85903-2 (PB)

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Contents

Foreword to the first English edition xiii

Preface to the first English edition xv

Preface to second edition xvii

Acknowledgments xix

Introduction xxi

PART 1 SEPARATION METHODS 1

1 General aspects of chromatography 31.1 General concepts of analytical chromatography 31.2 The chromatogram 61.3 Gaussian-shaped elution peaks 71.4 The plate theory 91.5 Nernst partition coefficient (K) 111.6 Column efficiency 121.7 Retention parameters 141.8 Separation (or selectivity) factor between two

solutes 171.9 Resolution factor between two peaks 171.10 The rate theory of chromatography 191.11 Optimization of a chromatographic analysis 221.12 Classification of chromatographic techniques 24

Problems 27

2 Gas chromatography 312.1 Components of a GC installation 312.2 Carrier gas and flow regulation 332.3 Sample introduction and the injection

chamber 342.4 Thermostatically controlled oven 392.5 Columns 392.6 Stationary phases 412.7 Principal gas chromatographic detectors 462.8 Detectors providing structural data 502.9 Fast chromatography 522.10 Multi-dimensional chromatography 532.11 Retention indexes and stationary phase constants 54

Problems 58

vi CONTENTS

3 High-performance liquid chromatography 633.1 The beginnings of HPLC 633.2 General concept of an HPLC system 643.3 Pumps and gradient elution 653.4 Injectors 683.5 Columns 683.6 Stationary phases 703.7 Chiral chromatography 753.8 Mobile phases 763.9 Paired-ion chromatography 783.10 Hydrophobic interaction chromatography 803.11 Principal detectors 803.12 Evolution and applications of HPLC 87

Problems 89

4 Ion chromatography 934.1 Basics of ion chromatography 934.2 Stationary phases 964.3 Mobile phases 984.4 Conductivity detectors 1004.5 Ion suppressors 1014.6 Principle and basic relationship 1044.7 Areas of the peaks and data treatment software 1054.8 External standard method 1054.9 Internal standard method 1074.10 Internal normalization method 110

Problems 112

5 Thin layer chromatography 1175.1 Principle of TLC 1175.2 Characteristics of TLC 1205.3 Stationary phases 1215.4 Separation and retention parameters 1225.5 Quantitative TLC 123

Problems 125

6 Supercritical fluid chromatography 1276.1 Supercritical fluids: a reminder 1276.2 Supercritical fluids as mobile phases 1296.3 Instrumentation in SFC 1306.4 Comparison of SFC with HPLC and GC 1316.5 SFC in chromatographic techniques 133

7 Size exclusion chromatography 1357.1 Principle of SEC 1357.2 Stationary and mobile phases 1377.3 Calibration curves 1387.4 Instrumentation 1397.5 Applications of SEC 140

Problems 143

CONTENTS vii

8 Capillary electrophoresis and electrochromatography 1458.1 From zone electrophoresis to capillary electrophoresis 1458.2 Electrophoretic mobility and electro-osmotic flow 1488.3 Instrumentation 1528.4 Electrophoretic techniques 1558.5 Performance of CE 1578.6 Capillary electrochromatography 159

Problems 161

PART 2 SPECTROSCOPIC METHODS 165

9 Ultraviolet and visible absorption spectroscopy 1679.1 The UV/Vis spectral region and the origin of the absorptions 1679.2 The UV/Vis spectrum 1699.3 Electronic transitions of organic compounds 1719.4 Chromophore groups 1739.5 Solvent effects: solvatochromism 1749.6 Fieser–Woodward rules 1769.7 Instrumentation in the UV/Visible 1789.8 UV/Vis spectrophotometers 1819.9 Quantitative analysis: laws of molecular absorption 1869.10 Methods in quantitative analysis 1909.11 Analysis of a single analyte and purity control 1929.12 Multicomponent analysis (MCA) 1939.13 Methods of baseline correction 1969.14 Relative error distribution due to instruments 1989.15 Derivative spectrometry 2009.16 Visual colorimetry by transmission or reflection 202

Problems 203

10 Infrared spectroscopy 20710.1 The origin of light absorption in the infrared 20710.2 Absorptions in the infrared 20810.3 Rotational–vibrational bands in the mid-IR 20810.4 Simplified model for vibrational interactions 21010.5 Real compounds 21210.6 Characteristic bands for organic compounds 21210.7 Infrared spectrometers and analysers 21610.8 Sources and detectors used in the mid-IR 22110.9 Sample analysis techniques 22510.10 Chemical imaging spectroscopy in the

infrared 23010.11 Archiving spectra 23210.12 Comparison of spectra 23310.13 Quantitative analysis 234

Problems 238

viii CONTENTS

11 Fluorimetry and chemiluminescence 24111.1 Fluorescence and phosphorescence 24111.2 The origin of fluorescence 24311.3 Relationship between fluorescence and concentration 24511.4 Rayleigh scattering and Raman bands 24711.5 Instrumentation 24911.6 Applications 25311.7 Time-resolved fluorimetry 25511.8 Chemiluminescence 256

Problems 259

12 X-ray fluorescence spectrometry 26312.1 Basic principles 26312.2 The X-ray fluorescence spectrum 26412.3 Excitation modes of elements in X-ray fluorescence 26612.4 Detection of X-rays 27112.5 Different types of instruments 27312.6 Sample preparation 27712.7 X-ray absorption – X-ray densimetry 27812.8 Quantitative analysis by X-ray fluorescence 27912.9 Applications of X-ray fluorescence 279

Problems 281

13 Atomic absorption and flame emission spectroscopy 28513.1 The effect of temperature upon an element 28513.2 Applications to modern instruments 28813.3 Atomic absorption versus flame emission 28813.4 Measurements by AAS or by FES 29013.5 Basic instrumentation for AAS 29113.6 Flame photometers 29713.7 Correction of interfering absorptions 29813.8 Physical and chemical interferences 30213.9 Sensitivity and detection limits in AAS 304

Problems 305

14 Atomic emission spectroscopy 30914.1 Optical emission spectroscopy (OES) 30914.2 Principle of atomic emission analysis 31014.3 Dissociation of the sample into atoms or ions 31114.4 Dispersive systems and spectral lines 31514.5 Simultaneous and sequential instruments 31714.6 Performances 32114.7 Applications of OES 323

Problems 324

15 Nuclear magnetic resonance spectroscopy 32715.1 General introduction 32715.2 Spin/magnetic field interaction for a nucleus 32815.3 Nuclei that can be studied by NMR 331

CONTENTS ix

15.4 Bloch theory for a nucleus of spin number I = 1/2 33115.5 Larmor frequency 33315.6 Pulsed NMR 33515.7 The processes of nuclear relaxation 33915.8 Chemical shift 34015.9 Measuring the chemical shift 34115.10 Shielding and deshielding of the nuclei 34215.11 Factors influencing chemical shifts 34215.12 Hyperfine structure – spin–spin coupling 34415.13 Heteronuclear coupling 34515.14 Homonuclear coupling 34715.15 Spin decoupling and particular pulse sequences 35215.16 HPLC-NMR coupling 35415.17 Fluorine and phosphorus NMR 35515.18 Quantitative NMR 35615.19 Analysers using pulsed NMR 360

Problems 364

PART 3 OTHER METHODS 367

16 Mass spectrometry 36916.1 Basic principles 36916.2 The magnetic-sector design 37216.3 ‘EB’ or ‘BE’ geometry mass analysers 37416.4 Time of flight analysers (TOF) 37916.5 Quadrupole analysers 38116.6 Quadrupole ion trap analysers 38516.7 Ion cyclotron resonance analysers (ICRMS) 38716.8 Mass spectrometer performances 38916.9 Sample introduction 39116.10 Major vacuum ionization techniques 39216.11 Atmospheric pressure ionization (API) 39716.12 Tandem mass spectrometry (MS/MS) 40116.13 Ion detection 40216.14 Identification by means of a spectral library 40416.15 Analysis of the elementary composition of ions 40516.16 Determination of molecular masses from multicharged ions 40716.17 Determination of isotope ratios for an element 40816.18 Fragmentation of organic ions 410

Problems 415

17 Labelling methods 41917.1 The principle of labelling methodologies 41917.2 Direct isotope dilution analysis with a radioactive

label 42017.3 Substoichiometric isotope dilution analysis 42117.4 Radio immuno-assays (RIA) 42217.5 Measuring radioisotope activity 42317.6 Antigens and antibodies 425

x CONTENTS

17.7 Enzymatic-immunoassay (EIA) 42617.8 Other immunoenzymatic techniques 42917.9 Advantages and limitations of the ELISA test in

chemistry 43017.10 Immunofluorescence analysis (IFA) 43117.11 Stable isotope labelling 43117.12 Neutron activation analysis (NAA) 432

Problems 437

18 Elemental analysis 44118.1 Particular analyses 44118.2 Elemental organic microanalysis 44218.3 Total nitrogen analysers (TN) 44518.4 Total sulfur analysers 44718.5 Total carbon analysers (TC, TIC and TOC) 44718.6 Mercury analysers 450

Problems 451

19 Potentiometric methods 45319.1 General principles 45319.2 A particular ISE: the pH electrode 45519.3 Other ion selective electrodes 45719.4 Slope and calculations 46019.5 Applications 463

Problems 463

20 Voltammetric and coulometric methods 46520.1 General principles 46520.2 The dropping-mercury electrode 46720.3 Direct current polarography (DCP) 46720.4 Diffusion current 46820.5 Pulsed polarography 47020.6 Amperometric detection in HPLC and HPCE 47220.7 Amperometric sensors 47220.8 Stripping voltammetry (SV) 47820.9 Potentiostatic coulometry and amperometric coulometry 48020.10 Coulometric titration of water by the Karl Fischer reaction 481

Problems 484

21 Sample preparation 48721.1 The need for sample pretreatment 48721.2 Solid phase extraction (SPE) 48821.3 Immunoaffinity extraction 49021.4 Microextraction procedures 49121.5 Gas extraction on a cartridge or a disc 49321.6 Headspace 49421.7 Supercritical phase extraction (SPE) 49621.8 Microwave reactors 49821.9 On-line analysers 498

CONTENTS xi

22 Basic statistical parameters 50122.1 Mean value, accuracy of a collection of

measurements 50122.2 Variance and standard deviation 50422.3 Random or indeterminate errors 50422.4 Confidence interval of the mean 50622.5 Comparison of results – parametric tests 50822.6 Rejection criteria Q-test (or Dixon test) 51022.7 Calibration curve and regression analysis 51122.8 Robust methods or non-parametric tests 51322.9 Optimization through the one-factor-at-a-time (OFAT)

experimentation 515Problems 516

Solutions 519

Appendix – List of acronyms 561

Bibliography 565

Table of some useful constants 567

Index 569

PART 1

Separation methods

0 2 4 6 8 10 12 14 16 18 min.

2 SEPARATION METHODS

The invention of chromatography

Who invented chromatography, one of the most widely used laboratory techniques? This questionleads to controversies. In the 1850s, Schönbein used filter paper to partially separate substancesin solution. He found that not all solutions reach the same height when set to rise in filterpaper. Goppelsröder (in Switzerland) found relations between the height to which a solutionclimbs in paper and its chemical composition. In 1861 he wrote ‘I am convinced that thismethod will prove to be very practical for the rapid determination of the nature of a mixture ofdyes, especially if appropriately chosen and characterised reagents are used’.

Even if both of them did valuable work towards the progress of paper chromatography, it istraditional to assign the invention of modern chromatography to Michael S. Tswett, shortly after1900. Through his successive publications, one can indeed reconstitute his thought processes,which makes of him a pioneer, even if not the inventor, of this significant separative method.His field of research was involved with the biochemistry of plants. At that time one could extractchlorophyll and other pigments from house plants, usually from the leaves, easily with ethanol.By evaporating this solvent, there remained a blackish extract which could be redissolved inmany other solvents and in particular in petroleum ether (now one would say polar or non-polarsolvents). However, it was not well understood why this last solvent was unable to directlyextract chlorophyll from the leaves. Tswett put forth the assumption that in plants chlorophyllwas retained by some molecular forces binding on the leaf substrate, thus preventing extractionby petroleum ether. He foresaw the principle of adsorption here. After drawing this conclusion,and to test this assumption he had the idea to dissolve the pigment extract in petroleumether and to add filter paper (cellulose), as a substitute for leaf tissue. He realized that papercollected the colour and that by adding ethanol to the mixture one could re-extract these samepigments.

As a continuation of his work, he decided to carry out systematic tests with all kinds ofpowders (organic or inorganic), which he could spread out. To save time he had carried outan assembly which enabled him to do several assays simultaneously. He placed the packedpowders to be tested in the narrow tubes and he added to each one of them a solution of thepigments in petroleum ether. That enabled him to observe that in certain tubes the powdersproduced superimposed rings of different colours, which testified that the force of retentionvaried with the nature of the pigments present. By rinsing the columns with a selection ofsuitable solvents he could collect some of these components separately. Modern chromatographyhad been born. A little later, in 1906, then he wrote the publication (appeared in Berichte desDeutschen Botanische Gesellshaft, 24, 384), in which he wrote the paragraph generally quoted:‘Like light rays in the spectrum, the different components of a pigment mixture, obeying alaw, are resolved on the calcium carbonate column and then can be measured qualitatively andquantitatively. I call such a preparation a chromatogram and the corresponding method thechromatographic method.’

1General aspects ofchromatography

Chromatography, the process by which the components of a mixture can beseparated, has become one of the primary analytical methods for the identificationand quantification of compounds in the gaseous or liquid state. The basic prin-ciple is based on the concentration equilibrium of the components of interest,between two immiscible phases. One is called the stationary phase, because it isimmobilized within a column or fixed upon a support, while the second, calledthe mobile phase, is forced through the first. The phases are chosen such thatcomponents of the sample have differing solubilities in each phase. The differ-ential migration of compounds lead to their separation. Of all the instrumentalanalytical techniques this hydrodynamic procedure is the one with the broadestapplication. Chromatography occupies a dominant position that all laboratoriesinvolved in molecular analysis can confirm.

1.1 General concepts of analytical chromatography

Chromatography is a physico-chemical method of separation of componentswithin mixtures, liquid or gaseous, in the same vein as distillation, crystallization,or the fractionated extraction. The applications of this procedure are thereforenumerous since many of heterogeneous mixtures, or those in solid form, canbe dissolved by a suitable solvent (which becomes, of course, a supplementarycomponent of the mixture).

A basic chromatographic process may be described as follows (Figure 1.1):

1. A vertical hollow glass tube (the column) is filled with a suitable finelypowdered solid, the stationary phase.

2. At the top of this column is placed a small volume of the sample mixture tobe separated into individual components.

Chemical Analysis: Second Edition Francis and Annick Rouessac© 2007 John Wiley & Sons, Ltd ISBN: 978-0-470-85902-5 (HB); ISBN: 978-0-470-85903-2 (PB)

4 CHAPTER 1 – GENERAL ASPECTS OF CHROMATOGRAPHY

Sample

MP

C

(a)

SP

MP

(c)

ba

c

Sample

MP

SP

(b)

Sample

(d)

ba

c

1 2 3...

Figure 1.1 A basic experiment in chromatography. (a) The necessary ingredients (C, column;SP, stationary phase; MP, mobile phase; and S, sample); (b) introduction of the sample; (c)start of elution; (d) recovery of the products following separation.

3. The sample is then taken up by continuous addition of the mobile phase,which goes through the column by gravity, carrying the various constituentsof the mixture along with it. This process is called elution. If the componentsmigrate at different velocities, they will become separated from each otherand can be recovered, mixed with the mobile phase.

This basic procedure, carried out in a column, has been used since its discoveryon a large scale for the separation or purification of numerous compounds(preparative column chromatography), but it has also progressed into a stand-aloneanalytical technique, particularly once the idea of measuring the migration times ofthe different compounds as a mean to identify them had been conceived, withoutthe need for their collection. To do that, an optical device was placed at thecolumn exit, which indicated the variation of the composition of the eluting phasewith time. This form of chromatography, whose goal is not simply to recover thecomponents but to control their migration, first appeared around 1940 though itsdevelopment since has been relatively slow.

The identification of a compound by chromatography is achieved by compar-ison: To identify a compound which may be A or B, a solution of this unknownis run on a column. Next, its retention time is compared with those for the tworeference compounds A and B previously recorded using the same apparatus andthe same experimental conditions. The choice between A and B for the unknownis done by comparison of the retention times.

In this experiment a true separation had not been effected (A and B were pureproducts) but only a comparison of their times of migration was performed. Insuch an experiment there are, however, three unfavourable points to note: theprocedure is fairly slow; absolute identification is unattainable; and the physicalcontact between the sample and the stationary phase could modify its properties,therefore its retention times and finally the conclusion.

1.1 GENERAL CONCEPTS OF ANALYTICAL CHROMATOGRAPHY 5

This method of separation, using two immiscible phases in contact with eachother, was first undertaken at the beginning of the 20th century and is credited tobotanist Michaël Tswett to whom is equally attributed the invention of the termschromatography and chromatogram.

The technique has improved considerably since its beginnings. Nowadayschromatographic techniques are piloted by computer software, which operatehighly efficient miniature columns able to separate nano-quantities of sample.These instruments comprise a complete range of accessories designed to assurereproducibility of successive experiments by the perfect control of the differentparameters of separation. Thus it is possible to obtain, during successive analysesof the same sample conducted within a few hours, recordings that are reproducibleto within a second (Figure 1.2).

The essential recording that is obtained for each separation is called achromatogram. It corresponds to a two-dimensional diagram traced on a chartpaper or a screen that reveals the variations of composition of the eluting mobilephase as it exits the column. To obtain this document, a sensor, of which thereexists a great variety, needs to be placed at the outlet of the column. The detectorsignal appears as the ordinate of the chromatogram while time or alternativelyelution volume appears on the abscissa.

� The identification of a molecular compound only by its retention time is somewhatarbitrary. A better method consists of associating two different complementarymethods, for example, a chromatograph and a second instrument on-line, such as a

a

Mobile Phase supply

Time

Inte

nsity

Chromatogram

Detector

b

or

0

1

1

22 33

Figure 1.2 The principle of analysis by chromatography. The chromatogram, the essentialgraph of every chromatographic analysis, describes the passage of components. It is obtainedfrom variations, as a function of time, of an electrical signal emitted by the detector. It isoften reconstructed from values that are digitized and stored to a microcomputer for repro-duction in a suitable format for the printer. (a). For a long time the chromatogram wasobtained by a simple chart recorder or an integrator (b). Right, a chromatogram illustratingthe separation of a mixture of at least three principal components. Note that the order ofappearance of the compounds corresponds to the relative position of each constituent on thecolumn.


mass spectrometer or an infrared spectrometer. These hyphenated techniquesenable the independent collating of two different types of information that are inde-pendent (time of migration and ‘the spectrum’). Therefore, it is possible to determinewithout ambiguity the composition and concentration of complex mixtures in whichthe concentration of compounds can be of the order of nanograms.

1.2 The chromatogram

The chromatogram is the representation of the variation, with time (rarely volume),of the amount of the analyte in the mobile phase exiting the chromatographiccolumn. It is a curve that has a baseline which corresponds to the trace obtainedin the absence of a compound being eluted. The separation is complete when thechromatogram shows as many chromatographic peaks as there are components inthe mixture to be analysed (Figure 1.3).

σ

100%

60.6

%50

%

13.5%

y

I I

(a) Retention time (b) Gaussian curve with μ = 20 and σ = 1

0.4

0 10 20 30

t ′R

tR Time0 tM (or t0)

(c) Normal Gaussian curve characteristics

0.399

0.2420.199

0.054

–2 0 1 +2O

w

w1/2

w1/2 = 2.35 σ

w = 4 σw = 1.7 w1/2

x

the area between –2 and +2accounts for 95.4% of thetotal area under the curveand bordered by the X axis

Figure 1.3 Chromatographic peaks. (a) The concept of retention time. The hold-up time tMis the retention time of an unretained compound in the column (the time it took to makethe trip through the column); (b) Anatomy of an ideal peak; (c) Significance of the threebasic parameters and a summary of the features of a Gaussian curve; (d) An example of areal chromatogram showing that while travelling along the column, each analyte is assumed topresent a Gaussian distribution of concentration.

1.3 GAUSSIAN-SHAPED ELUTION PEAKS 7

Gaussian

(d) Comparaison between a true chromatrogram and normal Gaussian-shaped peaks

Time

Figure 1.3 (Continued)

A constituent is characterized by its retention time tR, which represents the timeelapsed from the sample introduction to the detection of the peak maximum onthe chromatogram. In an ideal case, tR is independent of the quantity injected.

A constituent which is not retained will elute out of the column at time tM,called the hold-up time or dead time (formerly designated t0). It is the time requiredfor the mobile phase to pass through the column.

The difference between the retention time and the hold-up time is designatedby the adjusted retention time of the compound, t′

R.If the signal sent by the sensor varies linearly with the concentration of a

compound, then the same variation will occur for the area under the correspondingpeak on the chromatogram. This is a basic condition to perform quantitativeanalysis from a chromatogram.

1.3 Gaussian-shaped elution peaks

On a chromatogram the perfect elution peak would have the same form as thegraphical representation of the law of Normal distribution of random errors (Gaus-sian curve 1.1, cf. Section 22.3). In keeping with the classic notation, � wouldcorrespond to the retention time of the eluting peak while � to the standard devi-ation of the peak (�2 represents the variance). y represents the signal as a functionof time x, from the detector located at the outlet of the column (Figure 1.3).

This is why ideal elution peaks are usually described by the probability densityfunction (1.2).

y = 1

�√

2�· exp

[−�x − ��2

2�2

](1.1)

y = 1√2�

· exp

[−x2

2

](1.2)


This function is characterized by a symmetrical curve (maximum for x = 0,y = 0�3999) possessing two inflection points at x =+/ − 1 (Figure 1.3), for whichthe ordinate value is 0.242 (being 60.6 per cent of the maximum value). The widthof the curve at the inflection points is equal to 2�� = 1�.

In chromatography, w1/2 represents the width of the peak at half-height �w1/2 =2�35�� and �2 the variance of the peak. The width of the peak ‘at the base’ islabelled w and is measured at 13.5 per cent of the height. At this position, for theGaussian curve, w = 4� by definition.

Real chromatographic peaks often deviate significantly from the Gaussian idealaspect. There are several reasons for this. In particular, there are irregularities ofconcentration in the injection zone, at the head of the column. Moreover, thespeed of the mobile phase is zero at the wall of the column and maximum in thecentre of the column.

The observed asymmetry of a peak is measured by two parameters, the skewingfactor a measured at 10 per cent of its height and the tailing factor TF measuredat 5 per cent (for the definition of these terms, see Figure 1.4):

CM CM CM

CS CS CS

(a) (b) (c)

0

TF > 1a > 1

TF = 1 a = 1

TF < 1a < 1

Time Time Time

Concave isothermConvex isothermLinear isotherm

with : a = b/f at 10% h TF = (b + f)/2f at 5% h

10%

5%

100%

f b

Figure 1.4 Distribution isotherms. (a) The ideal situation corresponding to the invariance of theconcentration isotherm. (b) Situation in which the stationary phase is saturated – as a result ofwhich the ascent of the peak is faster than the descent (skewing factor greater than 1); (c) Theinverse situation : the constituent is retained too long by the stationary phase, the retention timeis therefore extended and the ascent of the peak is slower than the descent apparently normal. Foreach type of column, the manufacturers indicate the capacity limit expressed in ng/compound,prior to a potential deformation of the corresponding peak. The situations (a), (b) and(c) are illustrated by authentic chromatograms taken out from liquid chromatography technique.

1.4 THE PLATE THEORY 9

a = b

f(1.3)

TF = b + f

2f(1.4)

1.4 The plate theory

For half a century different theories have been and continue to be proposed tomodel chromatography and to explain the migration and separation of analytes inthe column. The best known are those employing a statistical approach (stochastictheory), the theoretical plate model or a molecular dynamics approach.

To explain the mechanism of migration and separation of compounds on thecolumn, the oldest model, known as Craig’s theoretical plate model is a staticapproach now judged to be obsolete, but which once offered a simple descriptionof the separation of constituents.

Although chromatography is a dynamic phenomenon, Craig’s model consideredthat each solute moves progressively along a sequence of distinct static steps. Inliquid–solid chromatography this elementary process is represented by a cycle ofadsorption/desorption. The continuity of these steps reproduces the migration ofthe compounds on the column, in a similar fashion to that achieved by a cartoonwhich gives the illusion of movement through a sequence of fixed images. Eachstep corresponds to a new state of equilibrium for the entire column.

These successive equilibria provide the basis of plate theory according to whicha column of length L is sliced horizontally into N fictitious, small plate-like discsof same height H and numbered from 1 to n. For each of them, the concentrationof the solute in the mobile phase is in equilibrium with the concentration of thissolute in the stationary phase. At each new equilibrium, the solute has progressedthrough the column by a distance of one disc (or plate), hence the name theoreticalplate theory.

The height equivalent to a theoretical plate (HETP or H) will be given byequation (1.5):

H = L

N(1.5)

This employs the polynomial approach to calculate, for a given plate, the massdistributed between the two phases present. At instant I , plate J contains a totalmass of analyte mT which is composed of the quantity mM of the analyte that hasjust arrived from plate J − 1 carried by the mobile phase formerly in equilibriumat instant I −1, to which is added the quantity mS already present in the stationaryphase of plate J at time I − 1 (Figure 1.5).

mT�I� J � = mM�I − 1� J − 1� + mS�I − 1� J �


Plate J–1

Plate J

Instant I–1 Instant l

(I, J)

(I, J–1)

Plate J + 1...

(l–1, J–1)

(l–1, J)

Figure 1.5 Schematic of a column cross-section.

If it is assumed for each theoretical plate that: mS = KmM and mT = mM + mS,then by a recursive formula, mT (as well as mM and mS), can be calculated. Giventhat for each plate the analyte is in a concentration equilibrium between the twophases, the total mass of analyte in solution in the volume of the mobile phase VM

of the column remains constant, so long as the analyte has not reached the columnoutlet. So, the chromatogram corresponds to the mass in transit carried by themobile phase at the �N + 1�th plate (Figure 1.6) during successive equilibria. Thistheory has a major fault in that it does not take into account the dispersion in thecolumn due to the diffusion of the compounds.

� The plate theory comes from an early approach by Martin and Synge (Nobellaureates in Chemistry, 1952), to describe chromatography by analogy with distillation

Compound A

Compound B

1 100

Con

cent

ratio

n (μ

g/m

L)

1

5

10

15

20

25

Elution fractions

Figure 1.6 Theoretical plate model. Computer simulation, aided by a spreadsheet, of theelution of two compounds A and B, chromatographed on a column of 30 theoretical plates�KA = 0�6KB = 1�6� MA = 300gMB = 300g�.The diagram represents the composition ofthe mixture at the outlet of the column after the first 100 equilibria. The graph shows thatapplication of the model gives rise to a non-symmetrical peak (Poisson summation). However,taking account of compound diffusion and with a larger number of equilibriums, the peakslook more and more like a Gaussian distribution.

1.5 NERNST PARTITION COEFFICIENT (K) 11

and counter current extraction as models. This term, used for historical reasons, hasno physical significance, in contrast to its homonym which serves to measure theperformances of a distillation column.

The retention time tR, of the solute on the column can be sub-divided intotwo terms: tM (hold-up time), which cumulates the times during which it isdissolved in the mobile phase and travels at the same speed as this phase, and tS

the cumulative times spent in the stationary phase, during which it is immobile.Between two successive transfers from one phase to the other, it is accepted thatthe concentrations have the time to re-equilibrate.

� In a chromatographic phase system, there are at least three sets of equilibria:solute/mobile phase, solute/stationary phase and mobile phase/stationary phase. Ina more recent theory of chromatography, no consideration is given to the idea ofmolecules immobilized by the stationary phase but rather that were simply sloweddown when passing in close proximity.

1.5 Nernst partition coefficient (K)

The fundamental physico-chemical parameter of chromatography is the equilib-rium constant K, termed the partition coefficient, quantifying the ratio of theconcentrations of each compound within the two phases.

K = CS

CM

= Molar concentration of the solute in the stationary phase

Molar concentration of the solute in the mobile phase(1.6)

Values of K are very variable since they can be large (e.g. 1000), when the mobilephase is a gas or small (e.g. 2) when the two phases are in the condensed state.Each compound occupies only a limited space on the column, with a variableconcentration in each place, therefore the true values of CM and CS vary in thecolumn, but their ratio is constant.

Chromatography and thermodynamics. Thermodynamic relationships can beapplied to the distribution equilibria defined above. K, �CS/CM�, the equilibriumconstant relative to the concentrations C of the compound in the mobile phase(M) and stationary phase (S) can be calculated from chromatography experiments.Thus, knowing the temperature of the experiment, the variation of the standardfree energy �G� for this transformation can be deduced:

CM ⇔ CS �G� = −RT ln K

In gas chromatography, where K can be easily determined at two differenttemperatures, it is possible to obtain the variations in standard enthalpy �H� andentropy �S� (if it is accepted that the entropy and the enthalpy have not changed):

�G� = �H� − T�S�


The values of these three parameters are all negative, indicating a spontaneoustransformation. It is to be expected that the entropy is decreased when thecompound moves from the mobile phase to the stationary phase where it is fixed.In the same way the Van’t Hoff equation can be used in a fairly rigorous way topredict the effect of temperature on the retention time of a compound. From thisit is clear that for detailed studies in chromatography, classic thermodynamics areapplicable.

d ln K

dT= �H

RT 2

1.6 Column efficiency

1.6.1 Theoretical efficiency (number of theoretical plates)

As the analyte migrates through column, it occupies a continually expanding zone(Figure 1.6). This linear dispersion �1 measured by the variance �2

1 increases withthe distance of migration. When this distance becomes L, the total column length,the variance will be:

�2L = H · L (1.7)

Reminding the plate theory model this approach also leads to the value of theheight equivalent to one theoretical plate H and to the number N , of theoreticalplates �N = L/H�.

Therefore (Figure 1.7), any chromatogram that shows an elution peak with thetemporal variance �2 permits the determination of the theoretical efficiency N for

Chromatogram

Col

umn

Eluent

Detector

Sig

nal

0

0 concentration

Ll σl

Time ttR

σ

Figure 1.7 Dispersion of a solute in a column and its translation on a chromatogram. Left,graph corresponding to the isochronic image of the concentration of an eluted compound ata particular instant. Right, chromatogram revealing the variation of the concentration at theoutlet of the column, as a function of time. tR and � are in the same ratio as L and �L. In theearly days the efficiency N was calculated from the chromatogram by using a graduated ruler.

1.6 COLUMN EFFICIENCY 13

the compound under investigation (1.8), and by deduction, of the value of Hknowing that H = L/N ;

N = L2

�2L

Or N = t2R

�2(1.8)

If these two parameters are accessible from the elution peak of the compound,just because tR and � are in the same ratio as that of L to �L.

On the chromatogram, � represents the half-width of the peak at 60.6 percent of its height and tR the retention time of the compound. tR and � shouldbe measured in the same units (time, distances or eluted volumes if the flowis constant). If � is expressed in units of volume (using the flow), then 4�corresponds to the ‘volume of the peak’, that contains around 95 per cent of theinjected compound. By consequence of the properties of the Gaussian curve (w =4� and w1/2 = 2�35�), Equation 1.9 results. However, because of the distortion ofmost peaks at their base, expression 1.9 is rarely used and finally Equation 1.10 ispreferred.

N is a relative parameter, since it depends upon both the solute chosen and theoperational conditions adopted. Generally a constituent is selected which appearstowards the end of the chromatogram in order to get a reference value, for lackof advance knowledge of whether the column will successfully achieve a givenseparation.

N = 16t2R

w2(1.9)

N = 5�54t2R

w1/22

(1.10)

1.6.2 Effective plates number (real efficiency)

In order to compare the performances of columns of different design for a givencompound – or to compare, in gas chromatography, the performances betweena capillary column and a packed column – more realistic values are obtained byreplacing the total retention time tR, which appears in expressions 1.8–1.10, by theadjusted retention time t′

R which does not take into account the hold-up time tM

spent by any compound in the mobile phase �t′R = tR − tM� The three preceding

expressions become:

Neff = t′2R

�2(1.11)

Neff = 16t′2R

w2(1.12)


Neff = 5�54t′2R

w1/22

(1.13)

Currently it is considered that these three expressions are not very useful.

1.6.3 Height equivalent to a theoretical plate (HETP)

The equivalent height of a theoretical plate H , as already defined (expression 1.5),is calculated for reference compounds to permit a comparison of columns ofdifferent lengths. H does not behave as a constant, its value depends upon thecompound chosen and upon the experimental conditions.

For a long time in gas chromatography an adjustment value called the effectiveheight of a theoretical plate Heff was calculated using the true efficiency.

This corresponds to the Equation 1.14;

Heff = L

Neff

(1.14)

In chromatography, in which the mobile phase is a liquid and the columnis filled with spherical particles, the adjusted height of the plate h, is oftenencountered. This parameter takes into account the average diameter dm of theparticles. This eliminates the effect of the particle size. Columns presenting thesame ratio (length of the column)/(diameter of the particles) will yield similarperformances.

h = H

dm

= L

Ndm

(1.15)

1.7 Retention parameters

Hold-up times or volumes are used in chromatography for various purposes,particularly to access to retention factor k. and thermodynamic parameters. Onlybasic expressions are given below.

1.7.1 Retention times

The definition of retention times, hold-up time, tM, retention time, tR and adjustedretention time, t′

R, have been given previously (paragraph 1.2).

1.7 RETENTION PARAMETERS 15

1.7.2 Retention volume (or elution volume) VR

The retention volume VR of an analyte represents the volume of mobile phasenecessary to enable its migration throughout the column from the moment ofentrance to the moment in which it leaves. To estimate this volume, differentmethods (direct or indirect) may be used, that depend of the physical stateof the mobile phase. On a standard chromatogram with time in abscissa, VR iscalculated from expression 1.16, if the flow rate F is constant,

VR = tR · F (1.16)

The volume of a peak, Vpeak corresponds to that volume of the mobile phase inwhich the compound is diluted when leaving the column. It is defined by:

Vpeak = w · F (1.17)

1.7.3 Hold-up volume (or dead volume) VM

The volume of the mobile phase in the column (known as the dead volume),VM, corresponds to the accessible interstitial volume. It is often calculated from achromatogram, provided a solute not retained by the stationary phase is present.The dead volume is deduced from tM and the flow rate F :

VM = tM · F (1.18)

Sometimes, in the simplest cases, the volume of the stationary phase designatedby VS can be calculated by subtracting the dead volume VM from the total internalvolume of the empty column.

1.7.4 Retention (or capacity) factor k

When a compound of total mass mT is introduced onto the column, it separatesinto two quantities: mM, the mass in the mobile phase and mS, the mass inthe stationary phase. During the solute’s migration down the column, these twoquantities remain constant. Their ratio, called the retention factor k, is constantand independent of mT:

k = mS

mM

= CS

CM

· VS

VM

= KVS

VM

(1.19)

The retention factor, also known as the capacity factor k, is a very importantparameter in chromatography for defining column performances. Though it does


not vary with the flow rate or the column length, k is it not a constant as it dependsupon the experimental conditions. For this reason it is sometimes designated byk′ rather than k alone.

This parameter takes into account the ability, great or small, of the column toretain each compound. Ideally, k should be superior to one but less than five,otherwise the time of analysis is unduly elongated.

An experimental approach of k can be as follows:Suppose the migration of a compound in the column. Recalling Craig’s model,each molecule is considered as passing alternately from the mobile phase (inwhich it progresses down the column), to the stationary phase (in which it isimmobilized). The average speed of the progression down the column is slowedif the time periods spent in the stationary phase are long. Extrapolate now to acase which supposes n molecules of this same compound (a sample of mass mT�.If we accept that at each instant, the ratio of the nS molecules fixed upon thestationary phase (mass mS� and of the nM molecules present in the mobile phase(mass mM�, is the same as that of the times �tS and tM� spent in each phase for asingle molecule, the three ratios will therefore have the same value:

nS

nM

= mS

mM

= tS

tM

= k

� Take the case of a molecule which spends 75 per cent of its time in the stationaryphase. Its average speed will be four times slower than if it rested permanently in themobile phase. As a consequence, if 4 μg of such a compound has been introducedonto the column, there will be an average of 1 μg permanently in the mobile phaseand 3 μg in the stationary phase.

Knowing that the retention time of a compound tR is such that tR = tM + tS, thevalue of k is therefore accessible from the chromatogram �tS = t′

R�; see Figure 1.7:

k = t′R

tM

= tR − tM

tM

(1.20)

This important relation can also be written:

tR = tM�1 + k� (1.21)

Bearing in mind the relations (1.16) and (1.18), the retention volume VR of asolute can be written :

VR = VM�1 + k� (1.22)

or

VR = VM + KVS (1.23)

This final expression linking the experimental parameters to the thermodynamiccoefficient of distribution K, is valid for the ideal chromatography.

1.9 RESOLUTION FACTOR BETWEEN TWO PEAKS 17

0 (or t0)

here,

α = 1.27

k2 = 3.92

k1 = 3.071

2

tM

tM

t ′R 1

tR1 tR2 Time

t ′R 2

α =t ′R 2t ′R1

k2 =t ′R 2t M

k1 =t ′R1t M

Figure 1.8 Retention factors and separation factor between two compounds. Each compoundhas its own retention factor. On this figure, the separation factor is around 1.3. The separationfactor is also equal to the ratio of the two retention factors. � alone is not enough to determinewhether the separation is really possible.

1.8 Separation (or selectivity) factor between twosolutes

The separation factor �, (1.24) enables the comparison of two adjacent peaks1 and 2 present in the same chromatogram (Figure 1.8). Using Equations 1.20and 1.19, it can be concluded that the separation factor can be expressed byEquation 1.25.

By definition � is greater than unity (species 1 elutes faster than species 2):

� = t′R�2�

t′R�1�

(1.24)

or

� = k2

k1

= K2

K1

(1.25)

For non-adjacent peaks the relative retention factor r, is applied, which is calculatedin a similar manner to �.

1.9 Resolution factor between two peaks

To quantify the separation between two compounds, another measure is providedby the resolution factor R. Contrary to the selectivity factor which does not takeinto account peak widths, the following expression is used to calculate R betweentwo compounds 1 and 2 (Figure 1.9):

R = 2tR�2� − tR�1�

w1 + w2

(1.26)


0.27

0.02

0.65

R = 0.75 R = 1 R = 1.5

1 1 1

Figure 1.9 Resolution factor. A simulation of chromatographic peaks using two identical Gaus-sian curves, slowly separating. The visual aspects corresponding to the values of R are indicatedon the diagrams. From a value of R = 1�5 the peaks can be considered to be baseline resolved,the valley between them being around 2 per cent.

0 5 10 15

3.7 min

7.5 min

15.3 min

20 min

60 m

30 m

15 m

R = 2.05

R = 2.91

R = 4.15

Figure 1.10 Effect of column length on the resolution. Chromatograms obtained with a GCinstrument illustrating that by doubling the length of the capillary column, the resolution ismultiplied by 1.41 or

√2 (adapted from a document of SGE Int. Ltd).

Other expressions derived from the preceding ones and established with a viewto replacing one parameter by another or to accommodate simplifications mayalso be employed to express the resolution. Therefore expression 1.27 is used inthis way.

1.10 THE RATE THEORY OF CHROMATOGRAPHY 19

It is also useful to relate the resolution to the efficiency, the retention factorand the separation factors of the two solutes (expression 1.28, obtained from1.26 when w1 = w2). The chromatograms on Figure 1.10 present an experimentalverification.

R = 1�177tR�2� − tR�1�

1 + 2

(1.27)

R = 1

4

√N2 · � − 1

�· k2

1 + k2

(1.28)

R =√

N

2· � − 1

�· k2 − k1

k1 + k2 + 2(1.29)

1.10 The rate theory of chromatography

In all of the previous discussion and particularly in the plate theory, the velocityof the mobile phase in the column and solute diffusion are, perhaps surprisingly,never taken into account. Of all things, the speed should have an influence uponthe progression of the analytes down the column, hence their dispersion and byconsequence, upon the quality of the analysis undertaken.

Rate theory is a more realistic description of the processes at work inside acolumn which takes account of the time taken for the solute to equilibrate betweenthe two phases. It is the dynamics of the separation process which is concerned.The first kinetic equation for packed columns in gas phase chromatography wasproposed by Van Deemter.

1.10.1 Van Deemter’s equation

This equation is based on a Gaussian distribution, similar to that of plate theory.Its simplified form, proposed by Van Deemter in 1956, is well known (expression1.30). The expression links the plate high H to the average linear velocity of themobile phase u in the column (Figure 1.11).

H = A + B

u+ Cu (1.30)

The three experimental basic coefficients A, B and C are related to diversephysico-chemical parameters of the column and to the experimental conditions.If H is expressed in cm, A will also be in cm, B in cm2/s and C in s (wherevelocity is measured in cm/s).


H = A + CuC

A B C

H (HETP) μm

14

12

10

8

6

4

2

00 20 40 60 80 100

B

A

CHm

in.

uopt.

uave.cm/s.

HA

HC

HB

H = HA + HB + HC

A, Packing term

B, Longitudinal diffusion term

C, Mass transfer term

A

too slowMobile phase

too rapid

B

Figure 1.11 Van Deemter’s curve in gas chromatography with the domains of parameters A,B and C indicated. There exists an equation similar to that of Van Deemter that considerstemperature: H = A + B/T + CT�

This equation reveals that there exists an optimal flow rate for each column,corresponding to the minimum of H , which predicts the curve described byEquation 1.30.

The loss in efficiency as the flow rate increases is obvious, and represents whatoccurs when an attempt is made to rush the chromatographic separation byincreasing the pressure upon the mobile phase.

However, intuition can hardly predict the loss in efficiency that occurs whenthe flow rate is too slow. To explain this phenomenon, the origins of the termsA, B and C must be recalled . Each of these parameters represents a domain ofinfluence which can be perceived on the graph (Figure 1.11).

The curve that represents the Van Deemter equation is a hyperbola which goesthrough a minimum �Hmin� when:

uopt =√

B

C(1.31)

Packing related term A = 2��dp

Term A is related to the flow profile of the mobile phase passing through thestationary phase. The size of the particles (diameter dp), their dimensional distri-bution and the uniformity of the packing (factor characteristic of packing �) can allbe the origin of flow paths of different length which cause broadening of the soluteband and improper exchanges between the two phases. This results in turbulentor Eddy diffusion, considered to have little importance in liquid chromatographyand absent for WCOT capillary columns in GC (Golay’s equation without termA, cf. paragraph 1.10.2). For a given column, nothing can be done to reduce theA term.

1.10 THE RATE THEORY OF CHROMATOGRAPHY 21

Gas (mobile phase) term B = 2�DG

Term B, which can be expressed from DG, the diffusion coefficient of the analytein the gas phase and �, the above packing factor, is related to the longitudinalmolecular diffusion in the column. It is especially important when the mobile phaseis a gas.

This term is a consequence of the entropy which reminds us that a system willtend spontaneously towards the maximum degrees of freedom, chaos, just as adrop of ink diffuses into a glass of water into which it has fallen. Consequently,if the flow rate is too slow, the compounds undergoing separation will mix fasterthan they will migrate. This is why one never must interrupt, even temporarily, achromatography once underway, as this puts at risk the level of efficiency of theexperiment.

Liquid (stationary phase) term C = CG + CL

Term C, which is related to the resistance to mass transfer of the solute between thetwo phases, becomes dominant when the flow rate is too high for an equilibrium tobe attained. Local turbulence within the mobile phase and concentration gradientsslow the equilibrium process �CS ⇔CM�. The diffusion of solute between the twophases is not instantaneous, so that it will be carried along out of equilibrium. Thehigher the velocity of mobile phase, the worse the broadening becomes. No simpleformula exists which takes into account the different factors integrated in term C.The parameter CG is dependent upon the diffusion coefficient of the solute in agaseous mobile phase, while the term CL depends upon the diffusion coefficientin a liquid stationary phase. Viscous stationary phases have larger C terms.

� In practice, the values for the coefficients of A, B and C in Figure 1.11 can beaccessed by making several measurements of efficiency for the same compoundundergoing chromatography at different flow rates, since flow and average linearspeed are related. Next the hyperbolic function that best satisfies the experimentalvalues can be calculated using, by preference, the method of multiple linearregression.

1.10.2 Golay’s equation

A few years after Van Deemter, Golay proposed a modified relationship reserved tocapillary columns used in gas phase chromatography. There is no A term becausethere is no packing in a capillary column (see paragraph 2.5.2).

H = B

u+ CLu + CGu (1.32)


Expression 1.33 leads to the minimum value for the HETP for a column of radiusr , if the retention factor of the particular compound under examination is known.

The coating efficiency can then be calculated being equal to 100 times theratio between the value found using expression 1.33 and that deduced from theefficiency �H = L/N� obtained from the chromatogram.

Htheo�min = r

√1 + 6k + 11k2

3�1 + k�2(1.33)

1.10.3 Knox’s equation

Another, more recent equation, the Knox equation, is applicable to various typesof liquid chromatography and includes the adjusted height h:

h = Au1/3 + B

u+ Cu (1.34)

1.11 Optimization of a chromatographic analysis

Analytical chromatography is used essentially in quantitative analysis. In orderto achieve this effectively, the areas under the peaks must be determined withprecision, which in turn necessitates well-separated analytes to be analysed. Acertain experience in chromatography is required when the analysis has to beoptimized, employing all available resources in terms of apparatus and softwarethat can simulate the results of temperature modifications, phases and otherphysical parameters.

� In gas phase chromatography, the separations can be so complex that it canbe difficult to determine in advance whether the temperature should be increasedor decreased. The choice of column, its length, its diameter, the stationary phasecomposition and the phase ratio (VM/VS) as well as the parameters of separation(temperature and flow rate), are amongst the factors which interact with each other.

The resolution and the elution time are the two most important dependentvariables to consider. In all optimizations, the goal is to achieve a sufficientlycomplete separation of the compounds of interest in the minimum time, thoughit should not be forgotten that time will be required to readjust the column to theinitial conditions to be ready for the next analysis. Chromatography corresponds,in fact, to a slow type of analysis. If the resolution is very good then optimizationconsists to save time in the analysis. This can be done by the choice of a shortercolumn – recalling that the resolution varies with the square root of the columnlength (cf. the parameter N of formula 1.28 and Figure 1.10).

1.11 OPTIMIZATION OF A CHROMATOGRAPHIC ANALYSIS 23

(b)

(a)

0 1 2 3 min

(c)

0 1 2 3 4 5 6 7 8 min

(d)

0 2 4 6 8 10 12 14 min0 1 2 3 4 5 min

Figure 1.12 Chromatograms of a separation. The mobile phase in each trace is a binary mixturewater/acetonitrile: (a) 50/50; (b) 55/45; (c) 60/40; (d) 65/35. The arrow indicates the dead timetM (min) (J.W. Dolan, LC-GC Int., 1994 7(6), 333).

Figure 1.12 shows the optimization of a separation, by liquid chromatography,of a mixture of aromatic hydrocarbons. In this case, optimization of the separationhas been carried out by successive modifications of the composition of the mobilephase. Note that by optimizing the sequence in this manner, the cycle time ofanalysis increases.

If only certain compounds present in a mixture are of interest, then a selectivedetector can be used which would detect only the desired components. Alternately,at the other extreme, attempts might be made to separate the largest number ofcompounds possible within the mixture.

Depending upon the different forms of chromatography, optimization can bemore or less rapid. In gas phase chromatography optimization is easier to achievethan in liquid chromatography in which the composition of mobile phase must

Resolution

Capacity Speed

1

2 3

Figure 1.13 The chromatographer’s triangle. The shaded areas indicate the domain corres-ponding to analytical chromatography based principally upon the five parameters K, N, k, �and R.


be considered: software now exists that can help in the choice of mobile phasecomposition. Based upon certain hypotheses (Gaussian peaks), the areas of poorlydefined peaks can be found.

The chromatographer must work within the limits bound by a triangle whosevertices correspond to three parameters which are in opposition: the resolu-tion, the speed and the capacity (Figure 1.13). An optimized analytical separationuses the full potential of the selectivity which is the most efficient parameter.In the chromatographer’s triangle shown, the optimized conditions are close tothe vertex of resolution.

1.12 Classification of chromatographic techniques

Chromatographic techniques can be classified according to various criteria: asa function of the physical nature of the phases; of the process used; or by thephysico-chemical phenomena giving rise to the Nernst distribution coefficient K.The following classification has been established by consideration of the physicalnature of the two phases involved (Figure 1.14).

1.12.1 Liquid phase chromatography (LC)

This type of chromatography, in which the mobile phase is a liquid belongs tothe oldest known form of the preparative methods of separation. This very broadcategory can be sub-divided depending on the retention phenomenon.

Liquid/solid chromatography (or adsorption chromatography)

The stationary phase is a solid medium to which the species adhere through thedual effect of physisorption and chemisorption. The physico-chemical parameterinvolved here is the adsorption coefficient. Stationary phases have made muchprogress since the time of Tswett, who used calcium carbonate or inulin (a veryfinely powdered polymer of ordinary sugar).

Ion chromatography (IC)

In this technique the mobile phase is a buffered solution while the solid stationaryphase has a surface composed of ionic sites. These phases allow the exchange oftheir mobile counter ion with ions of the same charge present in the sample. Thistype of separation relies on ionic distribution coefficients.

1.12 CLASSIFICATION OF CHROMATOGRAPHIC TECHNIQUES 25

Water soluble

Ionic

IC

HPLCIon pair

HPLCNormal phase

HPLCReversed phase

HPLCNormal phase

HPLCNormal phase

HPLCReversed phase

HPLCReversed phase

HPLCReversed phase

Non-ionic

Polar

M < 2000

Non-polar

Organosoluble

Organosoluble

Water soluble

ICM > 2000

SECGel filtration

SECGel permeation

SAMPLE

Figure 1.14 Selection guide for all of the different chromatographic techniques with liquid mobilephases. The choice of technique is chosen as a function of the molar mass, solubility and thepolarity of the compounds to be separated.

Size exclusion chromatography (SEC)

The stationary phase here is a material containing pores whose dimensions areselected as a function of the size of the species to be separated. This method


therefore uses a form of selective permeability at the molecular level leading to itsname, gel filtration or gel permeation depending on the nature of the mobile phase,which is either aqueous or organic. For this technique, the distribution coefficientis called the diffusion coefficient.

Liquid/liquid chromatography (or partition chromatography, LLC)

The stationary phase is an immobilized liquid upon an inert and porous material,which has only a mechanical role of support. Impregnation, the oldest procedurefor immobilizing a liquid on a porous material, is a method now abandonedbecause of the elevated risk of washing out the column, which is called bleeding.

Liquid/bound phase chromatography

In order to immobilize the stationary phase (generally a liquid polymer), it ispreferable to fix it by covalent bonding to a mechanical support. The qualityof separation depends upon the partition coefficient K of the solute between thetwo phases, a phenomenon comparable to a liquid-liquid extraction between anaqueous and organic phase in a separating funnel.

1.12.2 Gas phase chromatography (GC)

The mobile phase is an inert gas and as above this form of chromatography canbe sub-divided according to the nature of the phase components:

Gas/liquid/ chromatography (GLC)

As indicated above the mobile phase here is a gas and the stationary phase is animmobilized liquid, either by impregnation or by bonding to an inert supportwhich could be, quite simply, the inner surface of the column. This is the tech-nique commonly called gas phase chromatography (GC). The gaseous sample mustbe brought to its vapour state. It was Martin and Synge who, in 1941, suggestedthe replacement of the liquid mobile phase by a gas in order to improve the sepa-rations. From this era comes the true beginnings of the development of analyticalchromatography. Here once again it is the partition coefficient K that is involved.

Gas/solid chromatography (GSC)

The stationary phase is a porous solid (such as graphite, silica gel or alumina)while the mobile phase is a gas. This type of gas chromatography is very effective

PROBLEMS 27

for analyses of gas mixtures or of compounds that have a low boiling point. Theparameter concerned is the adsorption coefficient.

1.12.3 Supercritical fluid chromatography (SFC)

Here the mobile phase is a fluid in its supercritical state, such as carbon dioxideat about 50 �C and at more than 150 bar (15 MPa). The stationary phase can bea liquid or a solid. This technique combines the advantages of those discussedabove: liquid/liquid and gas/liquid chromatography.

Problems

1.1 A mixture placed in an Erlenmeyer flask comprises 6 mL of silica geland 40 mL of a solvent containing, in solution, 100 mg of a non-volatilecompound. After stirring, the mixture was left to stand before a 10 mLaliquot of the solution was extracted and evaporated to dryness. The residueweighed 12 mg.

Calculate the adsorption coefficient, K = CS/CM, of the compound inthis experiment.

1.2 The retention factor (or capacity factor), k of a compound is defined as k=mS/mM, that is by the ratio of the masses of the compound in equilibriumin the two phases. Show, from the information given in the correspondingchromatogram, that the expression used – k = �tR − tM�/tM – is equivalentto this. Remember that for a given compound the relation between theretention time tR, the time spent in the mobile phase tM (hold-up or deadtime) and the time spent in the stationary phase tS, is as follows:

tR = tM + tS

1.3 Calculate the separation factor (or selectivity factor), between twocompounds, 1 and 2, whose retention volumes are 6 mL and 7 mL, respec-tively. The dead volume of the column used is 1 mL. Show that this factor isequal to the ratio of the distribution coefficients K2/K1 of these compounds�tR�1� < tR�2��.

1.4 For a given solute show that the time of analysis – which can be comparedwith the retention time of the compound held longest on the column –depends, amongst other things, upon the length of the column, the average


linear velocity of the mobile phase and upon the volumes VS and VM whichindicate respectively the volume of the stationary and mobile phases.

1.5 Equation (2) is sometimes employed to calculate Neff . Show that this relationis equivalent to the more classical equation (1):

Neff = 5�54�tR − tM�2

w21/2

(1)

Neff = Nk2

�k + 1�2(2)

1.6 The resolution factor R for two solutes 1 and 2, whose elution peaks areadjacent, is sometimes expressed by equation (1):

R = tR�2� − tR�1�

w1/2�1� + w1/2�2�

(1)

R = 1

4

√N2

� − 1

�

k2

1 + k2

(2)

1. Show that this relation is different from the basic one by finding theexpression corresponding to the classic equation which uses wb, thepeak width at the baseline.

2. If it is revealed that the two adjacent peaks have the same width atthe baseline �w1 = w2�, then show that relation (2) is equivalent torelation (1) for the resolution.

1.7 1. Show that if the number of theoretical plates N is the same for twoneighbouring compounds 1 and 2, then the classic expression yieldingthe resolution, equation (1) below, can be transformed into (2).

R =√

N

2

k2 − k1

k1 + k2 + 2(1)

R = 1

2

√N

� − 1

� + 1

k

1 + k(2)

2. Show that if k= �k1 + k2�/2 then expressions (1) and (2) are equivalent.

PROBLEMS 29

1.8 The effective plate number Neff may be calculated as a function of theseparation factor � for a given value of the resolution, R. Derive thisrelationship.

Neff = 16R2 �2

�� − 1�2�

1.9 Consider two compounds for which tM = 1min, t1 = 11�30min and t2 =12min. The peak widths at half-height are 10 s and 12 s, respectively.Calculate the values of the respective resolutions using the relationshipsfrom the preceding exercise.

1.10 Certain gas phase chromatography apparatus allows a constant gas flow inthe column when operating under programmed temperature conditions.

1. What is the importance of such a device?

2. Deduce from the simplified version of Van Deemter’s equation for afull column the expression which calculates the optimum speed andwhich conveys a value for the HETP.

1.11 Explain how the resolution can be expressed in terms of the retentionvolumes in the following equation:

R =√

N

2

VR�2� − VR�1�

VR�1� + VR�2�

1.12 Which parameters contribute an effect to the widths of the peaks on achromatogram? Is it true that all of the compounds present in a sampleand which can be identified upon the chromatogram have spent the sameamount of time in the mobile phase of the column? Can it be said thata reduction in the retention factor k of a compound enhances its elutionfrom the column?

2Gas chromatography

Gas chromatography (GC) is a widely used technique whose first applications dateback more than 60 years. Since then, development has continued making the bestuse of the extreme sensitivity, versatility, the possibilities of automation and theease with which new analyses can be developed. Because separation of compoundmixtures on the column occurs while they are in the gaseous state, solid andliquid samples must first be vaporized. This represents, without hesitation, thegreatest constraint of gas phase chromatography and weighs against it, since itsuse is limited to the study of thermostable and sufficiently volatile compounds.However, the applications are numerous in all domains and the development ofhigh speed or multidimensional gas chromatography make this technique evenmore attractive. Its very great sensitivity permits detection of quantities of theorder of picograms for certain compounds.

2.1 Components of a GC installation

A gas chromatograph is composed of several components within a special frame.These components include the injector, the column and the detector, associatedwith a thermostatically controlled oven that enables the column to attain hightemperatures (Figure 2.1). The mobile phase that transports the analytes throughthe column is a gas referred to as the carrier gas. The carrier gas flow, which isprecisely controlled, enables reproducibility of the retention times.

Analysis starts when a small quantity of sample is introduced as either liquid orgas into the injector, which has the dual function of vaporizing the sample andmixing it with the gaseous flow at the head of the column. The column is usuallya narrow-bore tube which coils around itself with a length that can vary from1 to over 100 m, depending upon the type and the contents of the stationary phase.The column, which can serve for thousands of successive injections, is housed ina thermostatically controlled oven. At the end of the column, the mobile phase(carrier gas), passes through a detector before it exits to the atmosphere. Some gaschromatographs models of reduced size have their own electrical supply, enablingthem to operate in the field (see Figure 2.19).


32 CHAPTER 2 – GAS CHROMATOGRAPHY

Thermostated enclosure (–30∗, 450°C)

Injector COLUMN Detector

Data processing

Carrier gasexit

Sample inlet

Pressure regulationand flow regulation

Carrier gas supply

*or with cryogenic device from –80°C

1 Acetone2 2-Heptanone3 2-Octanone4 2-Nonanone5 2-Decanone6 2-Tridecanone7 2-Pentadecanone8 2-Heptadecanone

0 4

1

23

46

7

5

8

8 12 16 min

Mixture of methylketones

Phase: polysiloxane, film 0.25 μmColumn: 25 m, Int. Diam.: 0.22 mmTemp. from 60 up to 240°CSplit injection

Chromatogram

Figure 2.1 A GC installation. Schematic of a gas chromatograph. A commercial gas chromato-graph with a mass spectrometry system for detection (Model GCMS 5973 manufactured byAgilent Technologies). The instrument shown here is equipped with an auto-sampler. Below,the chromatogram for a mixture of ketones is displayed.

2.2 CARRIER GAS AND FLOW REGULATION 33

� In GC there are four operational parameters for a given stationary phase: L, lengthof the column, u, velocity of the mobile phase (which affects the theoretical effi-ciency N, see Section 1.6.1), T, temperature of the column and �, phase ratio (seeSection 2.6.4), which affects the retention factor k (Section 1.7.4). The operatingconditions of the chromatograph allows modifications in terms of T and u and there-fore affects both the efficiency of the column and the retention factors.

2.2 Carrier gas and flow regulation

The mobile phase is a gas (helium, hydrogen or nitrogen), either drawn froma commercially available gas cylinder or obtained, in the case of hydrogen ornitrogen, from an on-site generator, which provides gas of very high purity. Thecarrier gas must be free of all traces of hydrocarbons, water vapour and oxygen,because all of these may deteriorate polar stationary phases or reduce the sensitivityof detectors. For these reasons the carrier gas system includes filters containinga molecular sieve to remove water and a reducing agent for other impurities.The nature of the carrier gas has no significant influence upon the values of thepartition coefficients K of the compounds between the stationary and mobilephases, owing to an absence of interaction between the gas and solutes. By contrast,the viscosity of the carrier gas and its flow rate have an effect on the analytes’dispersion in the stationary phase and on their diffusion in the mobile phase (cf.Van Deemter’s equation), and by consequence upon the efficiency N and thesensitivity of detection (Figure 2.2). Hydrogen is the carrier gas of choice. If thisgas cannot be used for safety reasons, helium may be substituted.

Average linear velocities (cm/s)10 20 30 40 50 60 70 80 90

20

10

30

15

25

0.2

0.4

0.6

0.8

1.0

1.2HETP (mm)

(average values)

u

He

HeN2

N2

H2

H2

0 100 200 300Change in viscosity with T ( °C)

T (°C)

Vis

cosi

ty (

μPa

× s

)

u = L /tM

Figure 2.2 Efficiency as a function of the linear velocity of the carrier gas – viscosities of carriergases. These are typical Van Deemter curves showing that hydrogen, of the three gases studiedunder the same conditions, allows a faster separation, conveying a greater flexibility in termsof the flow rate, which is very useful for temperature programming. Note the increase in theviscosity of these gases with the temperature and that helium is more viscous than nitrogen atthe same temperature.


The pressure at the head of the column (several tens to hundreds of kPa) isstabilized either mechanically or through an electronic pressure control (EPC)in order that the flow rate remains constant at its optimal value. This device isvaluable because if the analysis is performed with temperature programming, theviscosity of the stationary phase and by consequence the loss of charge in thecolumn, increase with temperature. Therefore to maintain the carrier gas flowconstant, the pressure must be finely tuned to compensate this effect. The resultis a faster analysis and a longer life for the column.

The injector and the detector have dead volumes (hold-up volumes) which arecounted in the total retention volume. In GC, since the mobile phase is a gas,the flow rate measured at the outlet of the column should be corrected by acompression factor J , which compensates for the higher pressure at the head ofthe column (cf. expression 2.1).

If a chromatogram contains a peak for a compound that is not retained onthe stationary phase, it is possible to calculate the average linear velocity of theprogression, u, of the carrier gas. Elsewhere by installing a flow meter at the outletof the instrument (atmospheric pressure P0) and knowing the diameter of thecolumn the velocity u0 of the carrier gas, at the end of the column, can be deduced.The ratio between these two velocities is equal to J , the compression factor, whichis linked to the relative pressure P/P0 (P, the pressure at the head of the column):

J = u

u0

= 3

2· �P/P0�

2 − 1

�P/P0�3 − 1

(2.1)

2.3 Sample introduction and the injection chamber

2.3.1 Sample introduction

The most common injection method is where a microsyringe is used (Figure 2.3)to inject a very small quantity of sample in solution (e.g. 0�5�L), through a rubberseptum into a flash vaporizer port at the head of the column. For gaseous samples,

“open” needle

“plunger-in-needle” needle

syringe barrelplunger grip

plunger-in-barrel type

plunger-in-needle type

1 05μL10

0.1 00.51 μL

Figure 2.3 Typical syringes used in GC. Several models exist adapted to different types ofinjectors and columns. For some of them, (0.5 to 1�L), a plunger, pushed by the piston, entersthe needle to deliver all of the sample.

2.3 SAMPLE INTRODUCTION AND THE INJECTION CHAMBER 35

loop injectors are used similar to those described in liquid chromatography(cf. paragraph 3.4). To better control the reproducibility of the injections – simplychanging the user can lead substantial deviations, when in manual mode – mostinstruments are provides with autosamplers in which the syringe movements areautomated (Figure 2.1). The assembly operates in a cyclic fashion, taking thesample, injecting it rapidly (0.2 s) and rinsing the syringe. The latter is importantto avoid cross-contamination of successive samples that have similar composition.

� A sampling technique known as ‘headspace’, of which there are two modes, staticand dynamic, is very widespread in GC for the qualitative and even quantitativeanalyses of volatile constituents present in some samples (cf. Chapter 21).

2.3.2 Injectors

The injector, which is the sample’s entrance to the chromatograph, has differentfunctions. Besides its role as an inlet for the sample, it must vaporize, mix with thecarrier gas and bring about the sample at the head of the column. The characteristicsof the injectors, as well as the modes of injection, differ according to column type.The use of an automatic injection system can significantly enhance measurementprecision.

Direct vaporization injector

For packed and megabore columns (see paragraph 2.5), which typically use a flowrate of about 10 mL/min, direct vaporization is a simple way to introduce thesample. Any model of this type comprises a metal tube with a glass sleeve (calledthe insert). It is heated to the average boiling temperature of the compounds beingchromatographed. The needle of the micro-syringe containing the sample piercesthe septum, made of silicone rubber, which closes the end of the injector. The otherend, also heated, is connected directly to the column (Figure 2.4). Once all of theliquid plug has been introduced with a syringe it is immediately volatilized andenters the column entirely within a few seconds, swept along by the carrier gas.

Split/splitless injector

For capillary columns able to handle only a small capacity of sample, even thesmallest volume that it is possible to inject with a micro-syringe �0�1�L�, cansaturate the column. Special injectors are used which can operate in two modes,with or without flow splitting (also called split or splitless).

In the split mode a high flow rate of carrier gas arrives in the vaporizationchamber where it mixes with the vapours of injected sample (Figure 2.5). A vent


End of syringe

Carrier gas

Insert

Column

Cross sectionof a duckbill septum

Septum

Barrel of the injectorDuckbill-like aperture openseasily and seals reliably

O-Ring who sealsthe syringe needleduring injection

a Septum madeof silicon rubber

Screw top

Rubberseptum

Figure 2.4 Direct vaporization injector used for packed columns. Typical schematic of a modelemploying a septum. Depending upon the function required a wide range of inserts exist. Right,a variety of self-sealing septum (the ‘Microseal’ Merlin), which can be used thousands of times(reproduced courtesy of Agilent Technologies).

valve, regulated at between 50–100 mL/min, separates this flow into two fractions,of which the largest portion is vented from the injector, taking with it the majorityof the sample introduced. The split ratio typically varies between 1 : 20 and 1 : 500.Only the smallest fraction, containing an amount of sample equal to the ratio ofdivision, will penetrate into the column.

Split ratio = (split outlet flow rate + column outlet flow rate)

column outlet flow rate

When working with capillary columns, this type of injector is also used forvery dilutes samples in the splitless mode. In this mode a smaller volume ofsolution is injected very slowly from the micro-syringe during which bleedingvalve 2 (Figure 2.5) is maintained in a closed position for 0.5 to 1 minute in orderthat the vaporized mixture of compounds and carrier solvent are concentratedin the first decimetre of the column. The proper use of this mode of injection,which demands some experience, requires a program that starts with a coldertemperature in order that the solvent precedes the compounds onto the column.The re-opening of valve 2 provides an outlet for an excess of solvent-dilutedsample. Some less volatile compounds are eliminated and that can interfere withthe results of the analyses.

� In quantitative analysis, the use of the split/splitless injector can result in concentra-tion errors owing to a strong discrimination between compounds that are of differentvolatility: the composition of the fraction entering the column is different to that whichis eliminated from the injector. This mode of operation should be avoided when

2.3 SAMPLE INTRODUCTION AND THE INJECTION CHAMBER 37

Methadone (peak 3) and metabolites (peaks 1 & 2)

ef = 0.25 μm; Carrier gas He 40 cm/s

Inj. Splitless, 1 μL during 30 s

Capillary column DB 30 m, 320 μm inner diam.

T = 55°C for 1 min then 55 à 260°C at 30°C/min

Flame Ionisation Detector (FID)Make-up gas : nitrogen, 30 mL/min.

End of the syringe

Cooling air

Capillary column

(a)

(c)

(b)

1

2

3

Inlet valve

Rubberseptum

Carrier gasinlet

Glass liner(insert)

Split outlet

1

2

Septum purgevalve

Vapourisationchamber

Metal block

Figure 2.5 Injectors. (a) Above left, injection chamber. The carrier gas enters the chamberand can leave by three routes (when the injector is in split mode). A proportion of carrier gas(1) flows upward and purges the septum, another (2) exits through the split outlet (a needlevalve regulates the split) and finally a proportion passes onto the column. (b) Above right, coldinjection onto the column. (c) Below, a typical chromatogram obtained in splitless mode. Forsolvent peaks which are superimposed upon those of the compounds, a selective detector whichdoes not ‘see’ the solvent is recommended.

using an external standard (cf. paragraph 4.8). However this problem can be partiallycorrected by a good choice of the glass insert.

Cold on-column injection

This is not a vaporization technique. The sample is deposited directly into thecapillary column (‘cold on-column’ or COC). A special micro-syringe, whose needle(steel or silica) is of 0.15 mm diameter, is necessary for penetrating the columnwhich is cooled to 40 �C before being allowed to return to its normal operatingtemperature. This procedure, useful for thermally labile compounds or high boilingcompounds, is difficult to master without the aid of an autosampler. It is knownnot to discriminate between compounds of different volatilities (Figure 2.5).


Programmed temperature vaporization injector

This injector, named PTV (programmed temperature vaporizer), is conceptuallysimilar to the split/splitless model. The temperature of the injection chamber canbe programmed to effect a gradient, e.g. from 20 up to 300 �C, in a few tens ofseconds (Figure 2.6). So, the advantages of the split/splitless injection are combinedwith those of the cold injection onto the column.

It becomes possible to inject greater volumes with standard syringies avoidingneedle-induced discrimination. Furthermore, compounds having low boilingpoints (particularly solvents) can be eliminated.

The three principal modes of operation are named split cold injection, splitlesscold injection and injection with elimination of solvent.

• Split cold injection: the sample is introduced into the vaporization chamber andimmediately the vent valve is opened and the injector is heated. As the sampleis not instantaneously vaporized, the solvent and the different compoundspenetrate onto the column in the order of their boiling points. In this waythe column is never overcharged.

Rubberseptum

Heating

Glass wool

Cooling air

Cooling air

Septum purgevalve

Gas outlet

Gas inlet

Capillary column

Glass liner(Insert)

Figure 2.6 PTV injector. To modify very rapidly temperatures, the chamber of the injector issurrounded by an heating element or cooled by the circulation of a cold gas

2.5 COLUMNS 39

• Splitless cold injection: this mode is employed for trace analysis. The vent valveis closed during the injection. The injection chamber is then heated in orderto transfer the sample to the column, which is maintained cold.

• Injection with elimination of solvent: the sample is introduced into the coldinjector after which the vent valve is opened. Vent flow rate is very high andcan attain 1000 mL/min to eliminate all of the solvent. The injector is thenheated to permit transfer of the less volatiles compounds onto the column,the bleed valve now being closed (splitless mode). In this way it is possible toinject up to 50�L in a single injection or up to 500�L of sample solution,over several injections. This method eliminates the step of the preliminaryconcentration of sample prior to injection.

2.4 Thermostatically controlled oven

The gas chromatograph comprises an oven with sufficient volume to hold one ortwo columns easily and which can heat up to more than 400 �C. A weak thermalinertia permits a rapid but controlled temperature climb (gradient able to attain100 �C/min). The temperature must be controlled to within 0.1 �C in order toget reproducible separations in isothermal or temperature programmed modes.By installation of a cryogenic valve fed with N2 or CO2 in the liquid state, theoven can be regulated at low temperature.

2.5 Columns

There are two column types, which differ in their performance: packed columnsand capillary columns (Figure 2.7). For packed columns the stationary phase isdeposited or bonded by chemical reaction onto a porous support. For capillarycolumns a thin layer of stationary phase is deposited onto, or bound to the innersurface of the column.

2.5.1 Packed columns

These columns, less commonly used today, have diameters of 1/8 or 1/4 inch (3.18and 6.35 mm) and a length of between 1–3 m (Figures 2.7 and 2.8). Manufacturedfrom steel or glass, the internal wall of the tube is treated to avoid catalytic effectswith the sample. They can withstand a carrier gas flow rate within the range10–40 mL/min. They contain an inert and stable porous support on which thestationary phase can be impregnated or bounded (between 3 and 20 per cent).This solid support, having a specific surface area of 2–8m2/g, is made of spherical


Bondedphase

Silica glass

Polyimidecoating

(a) (b) (c)

Int. diam.0.15 mm

Stationnaryphase filling

Figure 2.7 Equal scale representation of main types of GC columns. (a) Steel column 3.18 mm;(b) ‘530’ column of 0.53 mm diameter; (c) capillary column of 0.2 mm diameter; (d) detail ofa capillary column. At this scale, the thickness of the stationary phase will scarcely be visible.The most common length is of 30 m.

Figure 2.8 Examples of packed (left) and capillary (right) columns (reproduced courtesy ofAlltech)

particles of around 0.2 mm diameter, which are obtained from diatomites, silicatefossils (kieselguhr, tripoli) whose skeleton is chemically comparable to that ofamorphous silica. A linker assures the cohesion of the grains. After calcinationthese diatomaceous earths are often designated by the name of Chromosorb®.Other synthetic materials have been developed such as Spherosil®, composed oftiny silica beads. All of these supports have a chemical reactivity comparable tosilica gel because of the presence of silanol groups.

Although the performance of packed columns is more modest than capillarycolumns, they are still usually employed for many routine analyses. Easy to manu-facture and with a large choice of stationary phases available, they are not however,well adapted to trace analyses.

2.5.2 Capillary columns (open tubular)

They are usually made of the highest purity fused silica obtained by the combustionof tetrachlorosilane �SiCl4� in an oxygen-rich atmosphere. The internal diameter of

2.6 STATIONARY PHASES 41

the tube used for these columns varies from 100 to 530�m, its thickness is 50�mand the length is of 12 to 100 m. These columns are rendered flexible by the appli-cation of a polyimide outer coating, a thermally stable polymer �Tmax = 370 �C� ora thin aluminium film. They have the advantages of physical strength and can bewound into coils around a lightweight metallic circular support (Figures 2.7 and2.8). Some manufacturers offer columns made from a metal capillary (aluminium,nickel or steel) which tolerates high operating temperatures of the order of 450 �C,providing that the stationary phase is stable enough. The internal surface of thecolumn is usually treated to favour a regular bonding for the stationary phase.This could be a chemical treatment (HCl at 350 �C), or the deposit of a thin layerof alumina or silica gel depending on the technique used to bond the stationaryphase. The thickness can vary between 0.05 and 5�m. These are WCOT (wall-coated open tubular) or PLOT (porous layer open tubular) columns dependingupon the nature of the stationary phase employed. Covalent bonding via Si–O–Si–C allows organic compounds to be bound to the silica surface. Columns areparticularly stable and can be rinsed periodically with solvents which enable themto recover their initial performance quality.

‘530�m’ columns

Constituted from a capillary of 0.53 mm internal diameter with length varyingfrom 5 to 50 m, these columns are designated, depending on the supplier, by theirprincipal characteristic ‘Widebore®’, ‘Megabore®’, or ‘Macrobore®’. They requirea carrier gas flow rate of at least 5 mL/min and can be as high to 15 mL/min, closeto that used in packed columns. However, the resolution and performance of thesecolumns are lower than that of capillary columns of smaller diameter. It is possibleto replace a packed column with a ‘530’ column on the older chromatographs,while retaining the same injectors, detectors and flow rates. Their main advantageover packed columns is their lack of bleeding, i.e. the progressive loss of thestationary phase with time. These columns are rarely packed columns.

� In order to deposit a film of known thickness, a method consists to fill the columnwith a solution of stationary phase of known concentration (e.g. 0.2 per cent in ether)so that the desired thickness is obtained after evaporation of solvent. This layer canthen be reticulated by a peroxide or by � irradiation. The procedure is similar to theapplication of a dye on a surface that has been treated beforehand to obtain a firmattachment.

2.6 Stationary phases

For packed columns, for which impregnation techniques are very simple, over 100stationary phases of various types have been proposed in the literature. On the


other hand, for bonded phase capillary columns the choice of stationary phase islimited because the generation of the film at the surface of the column requires adifferent principle than impregnation. The current phases correspond in principleto two families: the polysiloxanes and the polyethylene glycols. Each category canbe the object of minor structural modifications. For the study of optically activecompounds (enantiomeric separations), particular phases containing cyclodextrinsare used.

Each of these phases can be used between a minimum temperature beneathwhich concentration equilibria are too slow to occur, and a maximum temperatureabove which degradation of the polymer occurs. This high limit depends on thefilm thickness and the nature of the polymer.

The stationary phases described below are the more classical types, while in thecatalogues, phases especially adapted to particular applications can be found.Among them are phases for the separation of sulfur products, chlorinated pesti-cides, permanent gases, aldehydes, polycyclic aromatic hydrocarbons (PAH), etc.

2.6.1 Polysiloxanes

Polysiloxanes (also known as silicone oils and gums) are based upon a repetitivebackbone that consists of two hydrocarbon chains per silicon atom (Figure 2.9).There are about 20 different compositions of alkyl or aryl chains (methyl orphenyl) to which can be incorporated further functional groups (e.g. cyanopropyl,trifluropropyl). Monomers combined in variable proportions also convey changesin the properties of stationary phases (polarity, extended stability from −50 to300/325 �C, for the dimethylpolysiloxanes, depending on the column). Owing totheir very broad temperature range these phases are the most widely used.

A well-known phase which is used as a reference, since it is the only one thatis perfectly defined, is squalane, which on the McReynolds scale has a polarityof zero (cf. Section 2.10.3). This saturated hydrocarbon �C30H62� is derived fromsqualene, a terpenoid natural extract from shark’s liver (also present in the sebumof the skin). On this stationary phase, which can be used between 20 and 120 �C(following either deposition or impregnation), the compounds are eluted inincreasing order of their boiling temperatures, the retention time being inverselyproportional to the analyte vapour pressure. Diverse bonded phases based uponpolyalkylsiloxanes, almost apolar, can be used as a replacement for squalane.

2.6.2 Polyethyleneglycols (PEG)

The best known representative of this family is Carbowax® (Figure 2.8). Thesepolar polymers (Mr = 1500 to 20 000 – for the Carbowax 20M) can be used for


Polyethyleneglycols “carbowax ”

Si O

Me

Me

O Si

R1

R2

n m

Si

Me

Me

OSiO

OO

m

Si

OSi O

Si

OSiO

MeMe

Me

MeMeMe

Me

Me PolymerO

SiO

SiO

SiO

SiMe

Me

MeMeMeMe

O Me Me

SiO

SiO

SiO

SiO

SiOO

O C C

n

Method of formation of a bonded phase

T > 400°C

Wall of silica(capillary tube)

Silica wall

Bonded polysiloxanes (examples):

and numerous other phases with diverse chains

(CH2)3-CN or C2H4-CF3...

ex. R1 and R2 = Ph m = 95% and n = 5%

(–CH4)

H2 H2

Figure 2.9 Structure of polysiloxanes (silicones), and polyethylene glycols. An inventory of allthe compositions of this type of phase, used either for impregnation or bonding, would belengthy. Treatment of the internal wall of a silica column with tetradimethylsiloxane will obtaina stationary phase bounded, polymerized and later reticulated. (The bonding resembles thefixing of indelible colours in order to create a brightly tinted fabric: the colour contains anactive site with which is able to attach itself, for example, to the alcohol functionality of celluloseon cotton fibres).

deposition, impregnation or as bonded phases (40 < T < 240/260 �C, dependingon column diameter and film thickness).

2.6.3 Chiral stationary phases

These are generally polysiloxane basic phases mixed with 10 to 20 per cent byweight of �-cyclodextrin (polysaccharide) (Figure 2.10). This type of column issuitable for purifying racemic mixtures. If an organic compound, for example,comprises an asymmetric carbon the R and S enantiomers will not have the sameaffinity for the charged stationary phase in cyclodextrin, which also is expressedas two characteristc peaks. Therefore a chemical compound as a pure racematewill yield two peaks equal in size, each corresponding to an enantiomer (cf.paragraph 3.7).

Some columns accept high temperatures up to 450 �C (e.g. DEXSIL 400 orPETROCOL). Amongst the applications here is the analysis of the triglyceridesof fatty tissues and simulated distillation as in the petrol industry. The latter


2 - 3,3-dimethyl-2-butanol3 - Decane (C10)4 - 3-methyl-2-heptanone5 - 1-Hexanol6 - Undecane (C11)

1

2

3

4

5 10 150

795-

0637

Column β-DEX 120, 30 m × 0.25 mm Inner diam.; film 0.25 μmT = 80°C; FID detector; Inj. 1μl; split ratio 100: 1

1 - Nonane (C9)

5 6

min

Figure 2.10 Example of a separation with a chiral phase which contains cyclodextrins. Theuse of a chiral column to separate a racemic mixture of compounds leads to a splitting ofthe chromatogram signals as can be seen clearly for alcohols, 2 and 4. This chromatogramin isothermal mode, allows the calculation of retention indexes for the separated compounds(adapted from a Supelco illustration).

replaces the conventional distillation, which can take up to 100 hours per analysis(Figure 2.11).

2.6.4 Solid stationary phases

These phases are constituted from a variety of adsorbent materials: silica or aluminadeactivated by mineral salts, molecular sieves, porous glass, graphite (e.g. Chro-mosorb® 100, Porapak®). Capillary columns made by deposition of these materialsin the form of a fine porous layer are called PLOT. They are employed to sepa-rate gaseous or highly volatile samples. Columns containing graphitized carbonblack have been developed for the separation of N2, CO, CO2 and very lighthydrocarbons. The efficiency of these columns are very high (Figure 2.12).

Historically, silica gel, a thermostable material and insensitive to oxygen, wasone of the first compounds to serve as a solid stationary phase for GC columns(Figure 2.9). Today solid phases have become much more elaborate.

To compare or predict the behaviour of capillary columns it is useful to calculatethe phase ratio � = VM/VS (Figure 2.13). Calling dC the internal diameter of thecolumn and df the film thickness deposited on its inner surface, an approximatecalculation leads to:

� = VM

VS

= dC

4df

(2.2)

If the compounds to be separated are volatile, a column with a small phase ratioshould be chosen ��< 100� and vice versa. A column of 320�m with a stationary


712-

0546

1

2

3

4

5

6

7 8 9 10

50 480 50 480

250 320 450 570 650 700 750 250 320 450 570 650 700 750

Column HT-5, 6 m × 0.53 mm; film thickness: 0.1 μmColumn temp. 50 to 480°C (at 10°/min)

GC oven temperature GC oven temperature

analytes b.p. (°C)

1 - C20

10 - C1109 - C1008 - C907 - C806 - C705 - C604 - C503 - C402 - C30

Dis

tille

d m

ass

b.p. (°C)

Simulated distillation curve of an oil

Figure 2.11 Lubricating oil simulated distillation. The standard practice calls for the use of acolumn that can operate at high temperatures and of a series of known oligomers as boilingpoint references, to calibrate the retention times vs. boiling point curve. Next the sample “tobe distilled”, is chromatographed under the same programming conditions. A software packagemodels actual physical distillation, according to the data of the chromatogram. The distributioncurve is identical to that which would be obtained from the mixture if it was distilled, a labourintensive and much longer test (adapted from SGE 712-0546 and –0547 documents).

0 4 8 12 16 20 240

2

4

6

8

10

12

air C2H2C2H41951

Det

ecto

r si

gnal

Time (min)0 5 10 15 20 Min.

1

3

67

24

5

Column:Packing:

Temp:Flowrate:Detector:

30 ft × 1/8” OD30% DC-200 (500cstk)on Chromosorb® P-AW, 60/80

40°CHelium, 23 mL/minTCD

1 Nitrogen2 Methane3 Carbon dioxide4 Ethane5 Propane6 Iso-Butane7 n-Butane

Figure 2.12 Gas analyses: Left; one of the earliest ever chromatograms, obtained point bypoint and representing a mixture of air, ethylene and acetylene separated on silica gel (E. Cremerand F. Prior, Z. Elektrochem. 1951, 55, 66). Right; an analysis of gas on a modern packedcolumn (reproduced courtesy of the company Alltech).

phase of 1�m film thickness leads to a � ratio of 80 while for a column of 250�mwith a film thickness of 0�2�m, � = 310. Recalling that K = k�, it transpires thatk, for a given compound and a given stationary phase, will increase if � decreases.The � parameter, which is accessible from the physical characteristics of the


Silica glass

Polyimide coating

Stationary phase

dC, Column internal diameterdf, Film thickness

dc df

Figure 2.13 Capillary column section

column, allows the calculation of K, the distribution factor. Values are generallyvery large (e.g. 1000) owing to the nature of the mobile phase which in this caseis a gas.

2.7 Principal gas chromatographic detectors

Some detectors are universal; that is they are sensitive to practically everycompound that elutes from the column. On the other hand, there are discrimi-nating (selective) detectors that are sensitive only to specific compounds, yieldinga very uncomplicated chromatogram. The ideal situation to quantify an analyte,would be to have a detector which sees only this analyte. They can be also cate-gorized as destructive or non-destructive of the analytes.

Detectors are classified into two groups depending on whether they lead onlyto a single information such as the retention time and those which yield, besidesretention time, structural information of the analyte concerned. For this reason,some gas chromatographs are equipped with two or three detectors linked inseries (see Figure 2.17). Nonetheless, the response of all detectors is depen-dent on the molar concentration or on the mass of analyte in the carriergas.

2.7.1 Thermal conductivity detector (TCD)

This general purpose and non-destructive detector, in use since the early days ofGC, has for a long time remained a mainstay of the technique. Miniaturizationhas led to it being used as much for packed columns as for capillary columns. Ofmoderate sensitivity (400 pg/mL carrier gas) when compared with other detectors,it possesses nevertheless a very large linear range (six orders of magnitude). Itsoperating principle relies on the thermal conductivity of gas mixtures as a func-tion of their composition. The detector incorporates two identical thermistors,resembling minuscule filaments, placed in two tiny cavities of a metal block ther-mostatically maintained at a temperature above that of the column (Figure 2.14).

2.7 PRINCIPAL GAS CHROMATOGRAPHIC DETECTORS 47

Chromatogram

Signal

1

2

Catharometer block and its connections

Thermostated block

Upstreamside

Downstreamside

Carrier gas outletWire

Car

rier

gas

StabilisedPower Supply

SignalR3

R4

R2

R1Cathar .

1

2

GC composition

Injector

Flow restrictor

Column

Zerocontrol

Figure 2.14 Thermal conductivity detector. Left, schematic showing the carrier gas passage.Right, the cross-sectional scheme of the metal block with its operating principle, based on anelectrical Wheatstone bridge assembly (equilibrated when R1/R2 = R3/R4�.

Both thermistors are located within the path of the carrier gas. One is flushed bythe carrier gas evolving the column, while the other is flushed by a part of thecarrier gas entering the injector.

In the steady state a temperature equilibrium is established between thermalconductivity of the carrier gas and electrical current through the filament. Whena solute elutes there is a change in the mobile phase composition, which in turnmodifies its thermal conductivity. The thermal equilibrium being disrupted, thisresults in a variation of the resistance of one of the filaments which is proportionalto the concentration of the compound in the carrier gas.

2.7.2 Flame ionization detector (FID)

Considered as almost universal for organic compounds this is effectively thedetector par excellence, of GC. The gas flow issuing from the column passes throughthe flame of a small burner fed by a mixture of hydrogen and air. The detectordestroys the organic compound present whose combustion results in the releaseof ions and charged particles responsible for the passage of a very weak current�10−12 A� between two electrodes (pd of 100 to 300 V). One end of the burner, heldat ground potential, acts as a polarization electrode while the second electrode,called the collector, surrounds the flame rather like a collar. An electrometeramplifies the signal to a measurable voltage (Figure 2.15).

For organic compounds the intensity of the signal is considered to be propor-tional to the mass flow of carbon, excepted in the presence of heteroelements, suchas the halogens. Thus the area under the peak reflects the mass of the compoundeluted (dm/dt integrated between the beginning and end of the peak will give thetotal mass m). The sensitivity is expressed in Coulombs/g of carbon. The detectionlimit is in the order of 2 or 3 pg/s and the linear dynamic range attains 108. An


Electrometer Electrometer

+ 180 V

Signal

Signal

+ 300 V polarising voltage

Collectorelectrode

(a) (b)

Air

HydrogenMake-up gas

Alkalineceramic

Capillary columnNumerous variationsaccording to the suppliers

FID NPD

H2 or N2 (if capillary column)

Figure 2.15 FID detector (a) and NPD detector (b). The electrometers used with detectorsallow the measurement of very small intensities. The response of these mass flow dependantdetectors are unaffected by make-up gas.

FID detector is not affected by variations in flow rate which can lead to errorswith TCD.

In order to evaluate the presence of a volatile organic compound in polluted air(the VOCs), there exist portable instruments essentially housing a flame ionizationdetector that allows the measurement of the carbon content of the atmosphereexamined, without chromatographic separation.

2.7.3 Nitrogen phosphorus detector (NPD)

Compared with the FID, this thermoionic detector has a smaller flame in whichthe catalytic decomposition of compounds containing nitrogen (N), or phos-phorus (P) yields, fairly specifically, negative ions which are received by a collectorelectrode. As it appears on the representation (Figure 2.15), it comprises asmall ceramic cylinder doped with an alkaline salt (e.g. rubidium sulfate). Avoltage is applied to maintain a small plasma �800 �C� through the combus-tion of an air/hydrogen mixture. In these conditions the nitrogen present in airdoes not yield ions. Detector sensitivity is typically between 0.1 and 0.4 pg/s fornitrogen- or phosphorus-containing analytes, with a linear range of five orders ofmagnitude.

2.7.4 Electron capture detector (ECD)

This selective detector is considered to be excellent for trace analysis when analytescontain halogen atoms or nitro groups. A flow of nitrogen gas which has beenionized by electrons generated from a low energy �− radioactive source (a few

2.7 PRINCIPAL GAS CHROMATOGRAPHIC DETECTORS 49

mCi of 63Ni) passes between two electrodes maintained at a voltage differentialof around 100 V (Figure 2.16). At equilibrium, a base current I0 is generated,mainly due to free and very mobile electrons. If molecules (M), containing anelectrophore such an halogen (F, Cl, Br), cross the zone between the two electrodes,they capture thermally excited electrons to form heavy negative ions, which byconsequence are much less mobile, leading to a decrease in the signal.

N2

�−−→N+

2 + e−

M + e− −→ M−

M− + N+2 −→ M + N2

The measured intensity decreases exponentially by following a law of typeI = I0 exp�−kc. The linear range is of about four decades with nitrogen as thecarrier gas. The presence of a radioactive source in this detector means that it mustbe licensed (maintenance visits and regular area testing). This non-destructivedetector, well suited for compounds with high electron affinity, is mainly used foranalyses of chlorinated pesticides.

� Make-up gas. To provide maximum performances, the three detectors describedabove should be served with a gas flow of at least 20 mL/min, which is far superiorto that within capillary columns. This flow rate is attained by mixing, at the outlet ofthe column, a make-up gas either identical or different (such as nitrogen), from thecarrier gas.

+

–

CollectingelectrodePD ca. 50 V

Nitrogen outletRadioactivesource

63Ni

(a) (b)

Capillary column

Nitrogen flowing(make-up)

–

+

– – –

+ +

Ionisationchamber

Make-up gas

UV lamp

UV filter

Gas outletCapillary column inlet

Photons : 8.4 - 9.6 - 10 - 11.8 eV

Ionisation mechanism

ex. COXe, Ar...

+ 300 V

Anode

Cathode

hν

hν

M M

M

M

Analyte molecule

+ e(–)+

Figure 2.16 Electron capture detector(ECD) (a) and photo-ionization detector (PID) (b). TheECD must be installed in an well ventilated position owing to it containing a radioactive source.The PID contains a UV source from which the photons are emitted, having a pre-selectedenergy, using a filter which prevents undesired carrier gas ionization �M + h → M+ + e−�.Examples of filters: LiF at 11.8 eV, MgF2 at 9.6–10 eV, sapphire at 8.4 eV. On contact with theelectrodes the molecules return to uncharged state, ionization being therefore reversible. Theuse of the make-up gas provides an optimal flow.


2.7.5 Photo-ionization detector (PID)

This detector is fairly selective but it has only a narrow range of application,convenient for hydrocarbons as well as for S or P derivatives. The operatingprinciple consists to provoke ionization of the analytes by irradiation with a UVlamp emitting photons of high energy (of 8.4 to 11.8 eV). The photo-ionizationoccurs when the energy of the photon is greater to that of the first ionization ofthe compound (Figure 2.16). A photon of 9.6 eV can, for example, ionize benzene�PI1 = 9�2 eV� but not isopropanol �PI1 = 10�2 eV�. Electrons are collected by onan electrode linked to an electrometer.

This detector can function at more than 400 �C and is not destructive since theionization is reversible and affects only a small fraction of the molecules of eachcompound passing through. ECD and PID detectors are examples of class-specificdetectors often used in trace environmental analysis.

2.8 Detectors providing structural data

None of the detectors previously described yield any information as to the natureof the compound eluted. At most they are selective. Compounds identificationproceeds with the use of an internal calibration based on retention times orrequires the knowledge of retention indexes (cf. paragraph 2.10). When the chro-matogram is very complex, a confusion of identity could occur. To counteract this,several complementary detectors could be associated (Figure 2.17), or a detectorable to convey structural information based on spectroscopic data, or elementalcomposition of the analytes. The retention time and specific characteristics foreach compound could then be known. These detectors lead to stand-alone anal-ysis techniques for which the results depend only on the ability of the column toseparate properly the constituents of the sample mixture.

2.8.1 Atomic emission detector

The compounds coming out from the column enter into a microwave plasmawhose temperature is sufficient to create excited atoms (cf. Chapter 14). Thus,each element present in the solute eluted emits a characteristic spectrum, whichpermits its identification (see Figure 14.8).

2.8.2 Other detectors

A mass spectrometry detector (MSD) which consists of a low resolution mass spec-trometer, cf. Chapter 16) can be placed to the outlet of the column. A fragmenta-tion spectrum of each eluted compound is obtained. From the total ionic current

2.8 DETECTORS PROVIDING STRUCTURAL DATA 51

Analysis of a sample of watercontaining the 6 compoundsbelow using the headspaceprocedure instatic mode

1 - Dichloromethane2 - Butanone3 - 1,2-Dichloroethane4 - Toluene5 - m-Xylene6 - o-Dichlorobenzene

Conditions:Carrier gas: He, 2 mL/minColumn 30 m × 0.32 mm inner diam.Split ratio: 10/1Oven 50° C 1 min, then 10°C/min gradientup to 150°C

PID ECD FID

UV

1 2 3

3

3

4

5

6

0 10 20min

FID

PID 10,6 eV

ECD

1

1

2

2

4 5

6

6

Figure 2.17 Three detectors connected in series. At the outlet of a capillary column, eitherin series or in parallel and depending upon whether any of them destroy the sample, severaldetectors can be installed. Here, three chromatograms of an injected mixture are obtained fromeach detector. Note that the sensitivity varies significantly from one detector to another.

(TIC), a chromatogram can be traced which represents all of the compoundseluted. By choosing a particular ion (selective ion monitoring, or SIM), a selectivechromatogram can be produced. Although this method in some cases leads to amore modest sensitivity than with classic detectors, for many types of analyses ithas become essential, notably in the context of environmental studies. Neverthelessit requires the use of high performance columns �ID = 0�1–0�2mm� with very lowbleeding. Similarly with an infrared detector, the IR spectrum (cf. Ch. 10) can begraphically collated while with an ultraviolet detector (cf. Ch. 9), the correspondingUV spectrum of each compound eluted can be drawn. This is the domain ofcoupled ‘hyphenated’ methods, widely used for trace analyses. The modes of detec-tion mentioned above can be used jointly in the same installation equipped witha capillary column.


2.9 Fast chromatography

Conventional chromatography is a slow method of analysis. The retention timesare often longer than an hour when separating components of a complex mixture.To reduce these times, influence can be brought to bear upon several parameters.The most obvious requires the use of a shorter column and so as not to loseefficiency, the diameter of the capillary column should be reduced (cf. expression1.33). The stationary phase should be a thin film �0�1�m� and the columnmust operate with a steep programmed temperature gradient (e.g. 100 �C/min),now possible with modern GC instruments. Detector-response time also plays asignificant role in achieving the best peak fidelity.

If all the compounds in an existing GC run are too much separated, presentinglarge vacant spaces between peaks on the chromatogram, then the strategiesdescribed above should produce faster analysis times. This leads us to the domainof fast chromatography of volatile compounds which uses columns of very differentdesign, for example incorporating resistant outer coverings so that the tempera-ture �200 �C/20 s� might be increased more sharply. This also avoids to the ovena long time to cool down and get ready for the next run. As a result the retentiontimes are reduced significantly (Figure 2.18). This type of fast chromatographysometimes called high-speed GC finds its principal use in control analyses.

The detector must be able to store almost immediately the rapid variations inconcentration at the moment of each analyte’s elution. For detection by mass spec-trometry there is good reason to be attentive to the speed of the sweep of the m/zratio; a slow sequential sweep may lead to a situation in which the concentrationin the ionization chamber is not the same from one end of the recording to theother. The TOF-MS (cf. paragraph 16.5) does not suffer from this inconvenience.

There are now portable micro-chromatographs available weighing only a few kgfor the rapid analysis of gases and volatile products. Although containing a reser-voir of the carrier gas to assure their autonomy they are not bulky (Figure 2.19).

seconds

T °C

100

200

300

0 10 20 30 40 50

Figure 2.18 Fast chromatography. The graph records the programmed temperature of thecolumn

2.10 MULTI-DIMENSIONAL CHROMATOGRAPHY 53

1 - Methanol2 - Ethanol3 - Acetone4 - Pentane5 - Dichloromethane6 - Butanone7 -Trichloroethylene8 -Tetrachloromethane9 - Benzene

1

2 3

4

5

6

78

9

seconds0 10 20 30 40 50

Figure 2.19 Portable gas chromatograph. A lightweight (6.6 kg), battery operated, isothermalGC. This miniature analytical engine using a capillary column and a photoionization detectoris conceived for the analysis of gas and other volatile compounds (VOCs) (reproduced courtesyof Photovac). Below is an example of chromatogram obtained with such an instrument.

Certain components are obtained by micro-machining on silicon-chips.A short capillary column (5 m) is inserted into the outer metal sleeve, which isable to tolerate a rapid increase in temperature such as a gradient of 20 �C/s.The efficiency �N� remains fairly poor though the temperature gradient allows anoptimization of the selectivity between the compounds.

2.10 Multi-dimensional chromatography

In this technique, that has been used for a long time, the whole (or a fraction) firstcolumn effluent is analysed through a second column having different selectivities.This allows the resolution of analytes, which are not separated at the end ofthe first column. Called GC×GC or 2D-GC, the installation must comprise twodetectors and an injection valve between the two columns positioned in series(Figure 2.20).


Column A

Column B

Time Time

(b) Column(a) Column

C6H6

EtOH

EtOH + C6H6

Floodgate

Inj. n° 1

Det. n° 1

Det. n° 2

Inj. n° 2

Figure 2.20 GC × GC setup or two-dimensional chromatography. The arrangement of twocolumns each associated with a detector and an injection valve introduced between them. In theexample shown in (A), a polar column cannot separate ethanol and benzene. The correspondingfraction is therefore re-injected onto (b), a non-polar column, in which the separation is effected(figure courtesy of Thermoquest).

2.11 Retention indexes and stationary phase constants

These parameters have been developed to pursue at least three objectives:

• To identify a compound by a more general characteristic than its retentiontime under pre-defined controlled conditions. As a result, a system of retentionindexes has been developed which is an efficient and cheap means by whichto avoid certain identification errors.

• To follow the evolution over time of a column’s performance.

• To classify all stationary phases in order to simplify the choice of the columnbest adapted to a particular kind of separation problem. The chemical natureof the phases and polarities do not allow prediction of which column will beoptimal for a given separation. For this, the behaviour of stationary phaseswith respect to several reference compounds should be examined, preparingthe way toward stationary phase constants.

2.11.1 Kovats’ straight line relationship

The retention index related to a given stationary phase is determined as follows.When a mixture containing compounds belonging to a homologous series of

2.11 RETENTION INDEXES AND STATIONARY PHASE CONSTANTS 55

Retention time (min)

SPB-35 Column (Supelco),L = 30 m, T = 114°C, He gas.C10 (61)

C11 (113)

C12 (205)

C13 (371)C14 (666)

tR(n)tM(0)

(t ′Rn in Seconds)

logt ′Rn

0 2 4 6 8 10 12 1410 131211 14

1,5

1,7

1,9

2,1

2,3

2,5

2,7

2,9

Sol

vent

pea

k

Carbon number (n)

logt ′ Rn = 0,259n – 0,803

Figure 2.21 Kovats’ straight line graph. Left, isothermal chromatogram for a series of fiven-alkanes �C10 − C14�. Right, the corresponding plot of the Kovats’ relationship for the chosenstationary phase and for the pre-determined analytical conditions.

n-alkanes is injected onto a column maintained under isothermal mode, theresulting chromatogram is such that the logarithm of the adjusted retention timest′R�n� increases linearly with the number n of carbon atoms present in the corres-

ponding n-alkane (Figure 2.21).On a graphical representation, the carbon number n versus log t′

R�n� usuallyyields a series of well lined up points according to the following semi-empiricalmathematical relationship:

log t′R�n� = an + b (2.3)

The adjusted retention time t′R�n� corresponds to the retention time tR of an

alkane having n atoms of carbon, minus the dead time tM; a and b are numericalcoefficients. The slope of the graph obtained depends on the overall performanceof the column and the operating conditions of the chromatograph.

� This expression (2.3) follows on from another linear relation seen in ther-modynamics linking the variation in free energy and the equilibrium constant K,��G = −RT lnK), for a homologous family of compounds in which each term differsfrom the preceding one by a supplementary CH2 unit. Since K = k� therefore t′R =KtM/�, then log t′R will increase as ln K for the homologous family: ln t′R = ln K +�ln tM/��.

2.11.2 Kovats’ retention index (or indice)

A compound (X) is now injected onto the column without changing the tuning ofthe instrument. The resulting chromatogram will enable Ix, the Kovats’ retentionindex, to be calculated for X and the specific column employed: this is equal to100 times the equivalent number of carbon atoms nx of the ‘theoretical alkane’having the same adjusted retention time than X. Two methods can be used tofind nx:


• The first is based on the Kovats’ relationship previously obtained (Figure 2.21).This leads to a calculation of nx (therefore Ix).

• The second gives a good estimation of Ix from the adjusted retention timeof the two n-alkanes (n and n + 1C) that bracket compound X on thechromatogram:

Ix = 100n + 100log t ′

R�X� − log t ′R�n�

log t ′R�n+1� − log t ′

R�n�

�0�1 (2.4)

In contrast to the Kovats’ regression line, the retention index depends only onthe stationary phase and not on the column dimensions or the flow rate of thecarrier gas. Due to this the retention time is converted into a relative retention timeindependent of experimental conditions, but normalized to a series of paraffins.

In practice, to ensure of the experimental conditions for the two injec-tions are uniform, compound X and the the n−alkanes mixture are co-injected(Figure 2.22).

The chromatogram that gives the Kovats’ relationship for a given stationaryphase, can also serve to evaluate the performances of a column. For this, theseparation number also known as the trennzahl number (TZ) is calculated fromexpressions 2.5 or 2.6. The two retention times occurring in these relationshipsrelate to two successive alkanes differing by one carbon number (n and n + 1atoms) or to two compounds of a similar type. The separation number indicateshow many compounds could be baseline separated reasonably well by the columnin the interval of retention time of these two reference compounds. The alkanes

6

(1350)

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

7 8 9

2,65

3,03

Petrocol Column DH(Supelco),L = 50m, T = 60°C, He car. gas.

C6(390)

C8(938)

C9(1819)

C7(563)(731)

(tR Sec)

Tolu

ene

m-X

ylen

e

tM(281)

0 5 10 15 20 tR(n) 30 min. Itoluene = 757 Ixylene = 856

logt 'R(x)logt 'Rn

logt ' Rn = 0,382n-0,24

Carbon number (n)

Figure 2.22 Graphical measurement of Kovats’ retention index �I = 100nx� on a column in theisothermal mode. The number of equivalent carbons nx, is found from the logarithm of theadjusted retention time t′R of X. The chromatogram corresponds to the injection of a mixtureof 4 n-alkanes and two aromatic hydrocarbons. The values in italics match the retention timesgiven in seconds. By injecting periodically this mixture the modifications to the Kovats’ indexesof these hydrocarbons permits the following of the column’s performance. The calculationsfor retention indexes imply that the measurements were effected under isothermal conditions.With temperature programming they yield good results to the condition to adopt an adjustedformula, though this entails a reduction in precision.

2.11 RETENTION INDEXES AND STATIONARY PHASE CONSTANTS 57

whose elution times are either side of that of the compound being analysed arechosen. For the chromatogram of Figure 2.22, the TZ is around 30.

TZ = tR2 − tR1

�w1/2�1 + �w1/2�2

− 1 (2.5)

or

TZ = R

1�18− 1 (2.6)

There are tables of retention indexes of compounds currently in general useon the most common stationary phases. If several retention indexes of the samecompound obtained on different stationary phases are available, then this uniquecollection of values could then characterize the compound more precisely. Iden-tification by retention index is not as reliable as using more popular hyphenatedtechniques as GC/MS (cf. Section 2.8.2), but it requires a not inconsiderablematerial investment.

� Retention time locking. The identification of compounds for which the retentiontimes are very close and whose mass spectra are almost identical (certain formsof isomers) is obviously difficult. A current method consists of selecting an internalstandard or a compound known to be present in all of the samples to be analysedand through the use of computer software the value of its retention time is locked(unchangeable) for different analyses, even if undertaken on a different apparatus(but on the same stationary phase). The effect of this is to conserve equally theretention times of the other compounds of the mixture, facilitating their identification.This approach, which avoids referring to the retention index, is possible with modernGC instruments and is known as retention time locking (RTL).

2.11.3 McReynolds’ constants for stationary phases

To evaluate the behaviour of a stationary phase, a comparison of the Kovats’indexes for five reference compounds belonging to different structural classes ismade on the studied phase as well as on squalane, chosen as the reference standardphase for this calculation. The five indexes on a column using squalane, the onlyreproducible apolar phase since it is formed from a pure material, have beenestablished once and for all (Table 2.1).

The five McReynolds’ constants for a given stationary phase are obtained bycalculating the differences observed for each of the substances tested between theirKovats’ indexes on squalane �ISqualane� and that corresponding to the stationaryphase being studied �IPhase�:

McReynolds constant = �I = �IPhase − ISqualane� (2.7)

The sum of the five calculated values, using expression 2.7, has been used todefine the overall polarity of the phase under test study.


Table 2.1 McReynolds’ constants ��I� for several stationary phases normalized to squalane

Stationaryphase(symbol)

BenzeneX′

1-butanolY′

2-pentanoneZ′

NitropropaneU′

PyridineS′

Squalane 0 0 0 0 0SPB-Octyl 3 14 11 12 11SE-30 (OV-1) 16 55 44 65 42Carbowax 20M 322 536 368 572 510OV-210 146 238 358 468 310

Kovats’ index for the five reference compounds above �X′�Y′�Z′�U′�S′� on squalane

Isqualane 653 590 627 652 699

� Finally this method can tell if two phases should give comparable performancesor if a phase is better for an analyte with a specific functional group. Each of thetest compounds yields particular information regarding the stationary phase: benzenefor the inductive effect, pyridine for proton accepting, butanol for hydrogen bonding,nitropropane for dipolar interactions…

These constants, which are related to molecular structures, allow an appreciationof the interactive forces between stationary phase and solute as a function ofcompound class (Table 2.1).

An index whose value is high, suggests that the stationary phase strongly retainsthe compounds that contain the corresponding organic functions. This leads toan improved selectivity for this type of compound. In the same way, to separatean aromatic hydrocarbon from a mixture of ketones, a stationary phase would beselected for which the McReynolds’ constant for benzene is rather different to thatof pentanone. These differences in retention indexes are provide by suppliers.

The McReynolds’ constants have replaced Rohrschneider constants, which werebased upon the same principle though using partly different reference compounds.

Problems

2.1 Consider a GC capillary column where the length, diameter and thickness ofthe film of the stationary phase could all be modified (one factor at a timeand without adjustment of the apparatus’ physical characteristics, such astemperature and pressure, yet maintaining a flow such that the linear velocityof the gas remains the same).

The three parameters to be modified are displayed in the first column ofthe table below. Complete the different cases by indicating, using the symbolsprovided, the observations anticipated: + symbolises an increase, 0 shows aweak variation in either direction and − for a decrease.

PROBLEMS 59

Speed of separation Columncapacity

Retentionfactor, k

Selectivityfactor

Effectiveplatenumber,N

increase in column lengthincrease in column diameterincrease in film thickness

2.2 The best-known method for estimating the hold-up time, tM, consists ofmeasuring the retention time of a compound not retained upon the column.Described here is another method for calculating the hold-up time, whichrecalls the relation used in establishing factors of retention. Knowing thatfor a homologous series of organic compounds and where the temperatureof the column is constant, it can be written:

log�tR − tM� = a · n + b

(in which tR represents the total retention time of a compound having natoms of carbon, while a and b are constants which depend upon the typeof solute and the stationary phase chosen).

1. Recall the chromatographic parameters for which it is essential to knowthe hold-up time tM.

2. Give examples of compounds that might be used to determine tM in GC.

3. Calculate tM from the following experiment, employing the methodabove: A mixture of linear alkanes, possessing six, seven and eight atomsof carbon, is injected into the chromatograph. The total retention timesfor these compounds were respectively, 271 s, 311 s, and 399 s, under aconstant temperature of 80 �C. (Length of column 25 m, ID = 0�2mm,df = 0�2�m and the stationary phase is made up of polysiloxanes).

4. If the retention index for pyridine on squalane is 695, what is theMcReynolds constant of this compound on the column studied, if it isknown that under the conditions of the experiment, the retention timeis 346 s?

2.3 Find an expression to calculate the thickness of film df of a capillary columnfrom K, k and ID, (the column’s internal diameter).


A sample of hexane is injected onto a column having an internal diameterof 200�m for which K is equal to 250. The retention time for the hexaneis 200 s, while an unretained compound has a retention time of only 40 s.Calculate the film thickness df from this information.

Temperature of the column ��C�Compound b.p. � �C� −35 25 40

ethene −104 0.249 0.102 0.0833ethane −89 0.408 0.148 0.117propene −47 1.899 0.432 0.324propane −42 2.123 0.481 0.352

2.4 Show that for a capillary column, the average flow can be calculated fromthe following formula:

DmL/min = ucm/s × 0�47d2i mm

(where u represents the average linear velocity in a column of internaldiameter ID).

2.5 The table below contains values of the retention factor k for four refinerygases, studied at three different temperatures upon the same capillary column(length L= 30 cm, internal diameter = 250�m), whose stationary phase is oftype SE-30. The chromatograph is supplied with a cryogenic accessory.

1. Can the polarity or non-polarity of the phase SE-30 be deduced fromthe elution order of the compounds?

2. Calculate the selectivity factor for the couple propene–propane at thethree temperatures indicated.

3. Why for the same compound does k decrease in response to an increasein temperature?

4. What is the number of theoretical plates of the column for the propaneat 40 �C, if it is known that at this temperature the resolution factor forthe couple propene–propane=2?

5. What would be the minimum theoretical value of HETP for the propaneat 40 �C?

PROBLEMS 61

6. Supposing that the HETP resulting from the Van Deemter curve is thesame as that resulting from the calculation which might be performedwhen considering Question 4, calculate the coating efficiency.

7. If for a given compound, k is linked to the absolute temperature of thecolumn by the expression: ln k= �a/T�+b, find, for the case of ethane,numerical values for both a and b.

2.6 In a GC experiment a mixture of n-alkanes (up to n carbon atoms, where nrepresents a variable number) and butanol �CH3 CH2 CH2 CH2 OH� wereinjected onto a column maintained at a constant temperature and whosestationary phase was of silicone-type material. The equation of the Kovats’straight line derived from the chromatogram is: log t′

R = 0�39n− 0�29 (wheret′R the adjusted retention time is in seconds). The adjusted retention time

of butanol is 168 s. If it is known that the retention index for butanol ona column of squalane is 590 s then deduce its corresponding McReynoldsconstant upon this column.

2.7 A chromatogram reveals a resolution factor of 1.5 between two neighbouringpeaks, 1 and 2. If k2 = 5 and = 1�05, and knowing that the retention timeof the compound 2 is 5 min, then:

1. Calculate the hold-up time of this chromatogram.

2. What is the width of the second peak at half-height, if the scale of thechromatogram is such that 1 min corresponds to 1 cm?

Use the relation 1.28 (cf. paragraph 1.9)

3High-performance liquidchromatography

Of all the chromatographic techniques whose mobile phase is a liquid, high-performance liquid chromatography (HPLC) is perhaps the best known. Its fieldof applications overlaps a large section of gas phase chromatography, to whichcan be added the analyses of many compounds that are thermolabile, or verypolar or of high molecular weight. Its success is also due to the possibility, for thechromatographer, to act in a very precise manner upon the selectivity betweencompounds through an appropriate choice of columns and eluent composition byexploiting the solute/mobile phase/stationary phase interactions. Although the effi-ciency of the HPLC columns is less than those used for GC, new stationary phasesthat can operate in several modes such as ion pairing or increasing hydrophobicinteractions, reveal further possibilities of HPLC. Finally, miniaturization of thetechnique (nanochromatography) has facilitated its working association with massspectrometry.

3.1 The beginnings of HPLC

High-performance liquid chromatography, often called simply by its abbre-viation, HPLC constitutes a general purpose analytical technique derivedfrom the most ancient form of preparative liquid chromatography. Themodern day technique is greatly enhanced in terms of selectivity, resolution,through miniaturization and the use of very elaborate stationary phases. Thesephases comprise spherical micro-particles with diameters of 2–5�m, or porousmonolithic material that leads to a significant pressure drop on the column. A largepressure needs to be exerted upon the mobile phase to obtain a continuous flow.In spotting this particularity, the letter P of the abbreviation corresponded for along time to the word pressure.


64 CHAPTER 3 – HIGH-PERFORMANCE LIQUID CHROMATOGRAPHY

� The forced migration of a liquid phase in continuous contact with a stationaryphase is encountered in several chromatographic techniques. One of the aspectsparticular to HPLC is that of the partition mechanisms between analyte, mobilephase and stationary phase. They are based on coefficients of adsorptionor partition.

3.2 General concept of an HPLC system

An HPLC installation is composed of several specialized units which can be foundas separate entities or be integrated within a common framework, usually forreasons of hindrance (Figure 3.1). A tubing system of very small internal diameter(0.1 mm) assures the circulation of the mobile phase between the modules. These

Thermostattedcolumn compartment

UV Detector

1

2

3

4

5

Degasser

6

Solvent rack(mobile phase)

Analytical pump

Injector(autosampler)

Figure 3.1 Schematic of a modular HPLC instrument. A modular system allows users to adaptthe installation according to the applications to be carried out. The vertical assembly of thedifferent modules affords an economy of space. Here the chromatograph, model HP 1200,comprises an auto-sampler that allows continuous operation and a thermostatically-controlledcolumn to improve the reproducibility of the separations. (Reproduced courtesy of AgilentTechnologies).

3.3 PUMPS AND GRADIENT ELUTION 65

transfer tubes are made of stainless steel or of PEEK® (polyether-etherketone),a coloured and flexible polymer, able to resist the common solvents under highpressure (up to 350 bars).

� The low flow rates obey Poiseuille’s law. The maximum velocity of the mobilephase is found at the centre of the tubing while in contact with the wall it is zero. Thisproduces an inevitable dispersion of the compounds. To improve the separations thevolume of the mobile phase outside the column is maintained as low as possible (10per cent dead volume of the column).

3.3 Pumps and gradient elution

3.3.1 Pumps

All HPLC systems include at least one pump to force the mobile phase through thecolumn whose packing is fairly compact. The result of this is a pressure increaseat the injector which can attain 20 000 kPa (200 bars) depending upon the flowrate imposed upon the mobile phase, its viscosity, and the size of the particles ofthe stationary phase.

Pumps are designed in order to maintain a stable flow rate, avoiding pulsationseven when the composition of the mobile phase varies. These flow rate meteredpumps contain, in general, two pistons in series, working in opposition, to avoidinterruptions to the flow rate (Figure 3.2).

� The presence of a non-negligible quantity of ambient gases (N2, O2, CO2),dissolved in the solvents, can perturb the separations by modification of the compress-ibility of the mobile phases which leads to the eventual formation of bubbles. Inparticular, oxygen can interfere on the lifetime of the column while hindering theworking of both electrochemical and photometric UV detectors. The solvents aretherefore degassed either by ultrasound, rapid helium bubbling, or by diffusion forwhich they pass along a polymeric tube, of small diameter, permeable to gas, workinglike a membrane.

It is obvious that these pumps deliver a series of ‘pulses’ of the mobile phase.The perfecting of flow rate regulation is achieved by the insertion of a pressure(or pulse) damper, between the pump(s) and the injector. It operates on themechanical principle of ballasting. Several techniques have been developed toaccomplish this. The simplest mechanical ballasting consists of inserting betweenthe pump and the injector a large coil of narrow-bore tubing, several metres long.Under the influence of a wave of solvent the tubing unwinds slightly increasingits internal volume and counteracting the variation in pressure. The most usualdamper type is a membrane one (Figure 3.2), usually having a volume of around0.5 mL. The closed part is filled with heptane. Compressibility of this liquid isenough to compensate for the pulsations of the dual piston pump with pistonvolume around 100�L.


Mobile phase

Input valve

Proportioningvalve

Exit valve

Pulse damper

Outlet

Piston 2Piston 1

Seal

Towards injectorand column

Exit valve

Solvents (maximum 4)

A B

A B C D

Time

Flo

w r

ate

Heptane

Equilibration cylinderWorking cylinder

Vacuum degasser

Figure 3.2 Schematic of the dual-headed reciprocating pump. The most simplified way ofexplaining the cycle of operation, without taking into account the compressibility of the solvents,is as follows. From the moment when the outlet valve of cylinder A closes and its entrancevalve opens, the piston in A, moving backwards, sucks the eluent through the inlet check valveand the chamber fills. Meanwhile cylinder B is open and its piston moves forward to force themobile phase towards the injector and the column. The volume displaced by piston B is halfof that available in the chamber of piston A. With chamber A full, the entrance valve of Acloses and the corresponding outlet valve opens. Piston A now advances and pushes out thecontents of the chamber. Half of this volume is expelled directly towards the column, the otherhalf serves to fill cylinder B as piston B retracts. A pulse absorber is located between the twocylinders (diagram courtesy of Agilent Technologies). Below, graph showing variations in theflow rate as a function of movement of the pistons with time.

� To obtain micro flow rates (for example, 1 μL/min), necessary for a packed capillarycolumn, the same pumps are used, though with the addition at the outlet of a by-pass which divides the flow into two fractions of which only the smaller is directedtowards the column. To resist the low pHs of many elution mixtures, which can bemore corrosive when pressure is high, the components and surfaces that come intocontact with the mobile phase need to be inert. The pistons and valves of the pumpsare made of sapphire, agate, Teflon or special alloys.

Depending upon the design, an HPLC instrument contains generally two pistonsdriven by the same motor through a common eccentric cam; this allows onepiston to pump while the other is refilling (Figure 3.2). These pumps are asso-ciated with a mixing chamber and are located either just before or immediatelyfollowing. They are capable of delivering an eluent of fixed (isocratic mode), or

3.3 PUMPS AND GRADIENT ELUTION 67

of variable composition to create an elution gradient. For the second case thesystem must compensate for differences in solvent compressibility in order thatthe imposed composition be respected.

3.3.2 Low and high pressure gradients

If the composition of the mobile phase has to vary with time, as in a gradientelution, then several solvents are required, and in order to attain the desiredcomposition at a given pressure, the instrument must compensate for differencesin solvent compressibility. When the system contains a single pump, it shouldbe preceded by a low-pressure mixing chamber into which electronically activatedvalves permit to feed the solvents at a programmed composition. Alternately, in thehigh-pressure arrangement, installations contain more than one pump, dependingthe number of solvents. The final composition is obtained with a tee located afterthe pump but before the column (Figure 3.3).

When several analyses are to be done successively, one must avoid the use ofgradient elution, by seeking a practical compromise by means of a single eluentof fixed composition. This reduces post-analytical time after each analysis becausethe re-equilibration of the two phases to their initial composition, after a gradientelution, requires the passage of a volume of at least ten times the dead volume ofthe mobile phase.

Solvent A Solvent C

Solvent DSolvent B

Towards injectorand column

Pump 1 Pump 2

DamperMixing chamber(high pressure)

Figure 3.3 A schematic of the core of a high-pressure mixing (two-pump) system. The pumps arecalled binary, ternary or quaternary depending upon the number of solvents that can be mixedtogether (here binary). The mixing chamber, which controls the mobile phase composition, isat the output of the two high-pressure pumps on the downstream side of the pumps.


Set of loopsLoop

Manual valve

Figure 3.4 Injection valve for HPLC and an assortment of loops. Left, rear view of an injectionvalve (valve presenting 6 entries/outlets with a loop attached) ; Right, an assortment of loops ofdifferent volumes. The volume removed with the syringe must be of the order of 5 to 10 timesthat of the loop (reproduced courtesy of Rheodyne Inc.).

3.4 Injectors

In HPLC, the injection of a precise volume of sample onto the head of the columnmust be made as fast as possible in order to cause the minimum disturbanceto the dynamic regime of the mobile phase whose flow must be stable fromcolumn to detector. This is done by a special high pressure valve, either manual ormotorized, possessing several flow paths, which is situated just prior to the column(Figure 3.4). This must be a component of precision able to resist pressures greaterthan 30 000 kPa. The valve functions in two positions:

• In the load position only communication between the pump and the columnis assured (Figure 3.5). The sample, contained in a solution, is introduced atatmospheric pressure with the aid of a syringe into a small tubular curvedsection named a loop. Each loop has a small defined volume. They are eitherintegrated into the rotor of the valve or are connected to the outside of thevalve’s casing.

• In the inject position, the sample (which is in the loop) is inserted intothe flow of the mobile phase by the 60� rotation of a part of the valve,thus connecting the sample loop to the mobile phase circulation. Highlyreproducible injections are attained only if the loop has been completely filledwith the sample.

3.5 Columns

The column is a straight stainless steel calibrated tube which measures between3 and 15 cm in length and whose the inside wall is sometimes coated with aninert material such as glass or PEEK®. Stationary phase is held in the column

3.5 COLUMNS 69

Pump

Pump

Loop inlet

a model injector

Column

Column

CHARGELoop

Waste

Syringe needle

Loop

Towardscolumn

Towards pump

Syringe

INJECTION

1

1

2

2

3

3

4

4

5

5

6

6

(a)

(b)

Loop

Figure 3.5 The two steps of an injection incorporating a loop. (a) Loading of the loop; (b)Injection onto the column. Schematic of the model 7125 valve from Rheodyne Inc. Most of theinjectors are now automated.

between two porous discs situated at each of the extremities (Figure 3.6). Theinternal diameter of the column, for a long time standardized at 4.6 mm (requiringa mobile phase flow rate of between 0.5 to 2 mL/min) is now often narrower.A wide choice of column now exists with names such as narrow-bore (2–4 mmID), microbore (1–2 mm), packed capillaries �< 1mm�, for which the flow rate

Guard column holder

Guard cartridge

Sintered disk

Cartridge column

End fittingfor connection

Figure 3.6 Standard column and guard column for HPLC. View of the ZORBAX®columnassembly and its exploded view. The replaceable precolumn prevents clogging of the analyticalcolumn while extending its lifetime and preserving its performance (Reproduced courtesy ofRTI).


0 10 20min

a

b

c

Figure 3.7 The effect of column temperature upon compound separation. Analysis of acompound mixture using the same mobile phase flow rate at three different temperatures(a) 25�C, (b) 35�C, (c) 45�C.

descends to a few �L/min and therefore requires special pumps and detectors.These narrow columns not only substantially reduce the amount of mobile phase –just a few drops being sufficient to elute all of the compounds – , but also improveresolution by diminishing the diffusion inside the column. They equally have agreater sensitivity and allow HPLC-MS combination (cf. Chapter 16).

In order to extend the lifetime of the column, it is often preceded by a precolumnor guard column, short (0.4 to 1 cm), and packed with the same stationary phase asthe analytical column (Figure 3.6). This precolumn, which retains the compoundsof Rf = 0, is periodically changed. It is also recommended, prior to analysis, topass the samples solutions through a filter of pore size less than 0�5�m.

The influence of temperature upon the quality of separation was for a longtime neglected. Now, HPLC instruments are equipped with columns (and there-fore eluents) whose temperature is thermostatically controlled. This enhances thereproducibility of analyses and offers a further parameter of separation to beconsidered (Figure 3.7).


The stationary phase (SP) in contact with the mobile phase (MP) is the secondmedium with which the compounds initially dissolved in the mobile phase willinteract. On the column there will be as many particular associations of the threeconstituents [MP/compound/SP] as there are analytes in the sample.

Many organic and inorganic materials have been tested for use as packing forcolumns.


3.6.1 Silica gel, the major material for current phases

For the majority of applications silica gel still represents the basic material used topack HPLC columns. It is a rigid, amorphous solid having a composition formulaSiO2�H2O�n (where n is very close to 0), quite different from natural crystallinesilica �SiO2�, which is only a distant precursor of it. Silica gel is in the form ofspherical particles, sometimes porous, with a diameter of between 2 to 5�m. Thisassures a compact and homogeneous packing of the column which allows a regularcirculation of the mobile phase without the formation of preferential routes in thecolumn (Figure 3.8).

It is prepared under conditions of controlled hydrolysis, by a sol–gelpolymerization of an alkoxysilicate (e.g. tetraethoxysilane) in the form of anemulsion, under the effect of base-catalysed hydrolysis. Initially, tiny particles areformed �0�2�m� which grow in a regular manner, by various methods, to formspheres that attain a few micrometres in diameter.

� Recently a new type of column has appeared. Named monolithic it is packed with aporous silica gel which unites to form a single entity (Figure 3.8). This material, morepermeable to solvents than traditional bead type stationary phases, conserves a highefficiency even for rapid flow rates of the mobile phase. These columns, now fullyreproducible, have equivalent performances to packed columns.

Silica gel is a very polar material corresponding to a three-dimensional network.Though it does not possess the well-ordered structure of crystalline silica, it doesmaintain the tetrahedral arrangement of four bonds around the silicon atom.This is a reticulated inorganic polymer (Figure 3.8) containing a variable numberof silanol groups, which have resisted the final calcination. These silanol groupsare responsible for the acidic catalytic effect of this material because Si-OH hasa pKa of 10, comparable with that of phenol. To measure the concentration ofsilanol groups, solid state 29Si nuclear magnetic resonance (NMR) can be used,or alternatively, in an indirect manner, by quantifying the carbon content for thecovalently bound phases.

The characteristics of a silica gel depend upon several parameters, amongstwhich are the internal structure, the size of the particles, the porosity (dimensionand distribution of the pores) the specific area, the resistance to crushing and thepolarity. Common silica gels used in HPLC contain around five silanol groupsper �m2. The specific area is of the order of 350m2/g. They can be non-porousor porous (pore size of around 10 nm). The volume of the mobile phase on thecolumn varies from 30 to 70 per cent of the column’s total volume. This hascome far from the phases used at the beginning of the last century by Tswett,which were of chalk dust or powdered sugar. The treatment to which the silica issubmitted makes it something rather like magic sand!

� The preparation of silica gel in the form of irregular grains, used in preparative chro-matography, proceeds in a different fashion. First, orthosilicic acid is formed which


comprises the unstable [Si(OH)4], by acidification using sodium silicate [Na2SiO3](old name ‘pebble liquor’ or water-glass) obtained from definite purified sands byalkaline fusion. This unstable orthosilicic acid initially dimerizes then poly-condensesprogressively to colloidal particles having a hydroxylated surface. Through aggrega-tion a hydrogel of gelatinous silica is obtained, the calcination of which yields densegrains of silica gel (xerogel). Some of the reactions involved here are similar to thosewhich are encountered for the preparation of the microspheric solid phases used foranalytical chromatography.

Siloxane bond Silanol group(isolated)

(f)

Silanol group(twin)

(a) (b)

(d)

(c)

(e)

SiOO O

O

O

O

HO

OH

OH

OHOH

OHOH

Si

SiO

O

O

OO

O

O

OOO

O

O

OSi

Si

Si

Si

Si

Si

Si

Si

SiSi

SiSi

HO

HO

Urea/formaldehydesolution, pH = 2

Matrix polymerurea-formaldehydeSol-gel particlesTetraethoxysilane Diam. 3–6 μm

EtO Si

OEt

OEt

OEtH2O

—SiO2—

Heat with O2

Figure 3.8 Silica gel for chromatography. (a) Crude molecular diagram presenting the 3D-structure of a silica gel containing silanol groups. This material must be very pure, traces ofmetallic elements can increase the acidity of the silanol groups. (b) Porous particle (c) Non-porous particle used for rapid separations. (d) Electron microscopic images of silica gel particles.(e) Monolithic silica gel (reproduced courtesy of Merck). (f) Preparation of spherical grainsof silica gel via a sol–gel. The dispersive medium, called sol, is made of spherical particlesthat are only a few nanometres in diameter. The small spheres agglutinate in the presenceof a urea/formaldehyde binding agent until the requisite size �3–7�m� is attained. The finaltreatment is a pyrolysis to eliminate the organic matrix.


Partitionchromatography

Adsorptionchromatography

ABSORPTION ADSORPTION

Phase 2Phase 1Phase 2Phase 1

Figure 3.9 The phenomena of adsorption and partition. Contrary to absorption, adsorption isa surface phenomenon. Separation is due to a series of adsorption/desorption steps. Absorptionis due to solute partitioning between the two phases.

SiO2 + NaOH −→ Na2SiO3 + H2O

Na2SiO3

H3O+−→ �Si�OH�4�

−H2O−→orthosilicic acid1

��HO�3SiOSi�OH�3�−nH2O−→

orthosilicic acid2

�SiO2�n · �H2O�x‘silica gel’

The mode of action of silica gel is founded upon adsorption (Figure 3.9),a phenomenon that leads to the accumulation of a compound at the interfacebetween the stationary and mobile phases. In simpler cases, a monolayer is formed(known as a Langmuir isotherm), though often some attraction and interactionoccurs between the molecules already adsorbed and those still in solution. Thiscontributes to the asymmetry of the elution peaks. Other theories explain theseparation phenomenon by a simple slowing down (continuously), at the interfaceMP/SP which is different for each analyte.

3.6.2 Bonded silica

Though possessing a large capacity for adsorption, silica gel in its simplest state,as described previously, is used less and less for analysis since its qualities changewith time, resulting in a lack of reproducibility of separations. For many appli-cations it must be, at least, rehydrated (3–8 per cent water) in order to bedeactivated.

To remedy this situation and reduce the often excessive gel’s polarity, the silanolgroups are exploited in order to provide sites of covalent bonding for organicmolecules. Bonded silica gel, modified in this way, behave as a liquid in thatthe separation mechanism now depends on the partition coefficient instead ofadsorption coefficient. These covalently bonded phases, whose polarity can be easilyadjusted, constitute the bases of the reversed phase polarity partition chromatographyor RP-HPLC, used in the majority of HPLC separations. Two types of syntheseslead to monomeric or polymeric bonded surfaces:

• Monomeric phases (10–15�m thickness): They are obtained by reactionof an alkyl-monochlorosilane in the presence of an alkaline agent with


surface silanol groups (Figure 3.10). The RP-8 (dimethyloctylsilane) or RP-18(dimethyloctadecylsilane groups, ODS) are prepared in this way. However,a part of the Si-OH groups remain intact and can be the origin of inter-fering polar interactions. A more complete reaction is obtained with othersilyl reactants such as chlorotrimethylsilane �ClSiMe3� or hexamethyldisi-lazane �Me3SiNHSiMe3�. The sites that remain non-transformed are usuallyas inaccessible to the reactants as they are to the analytes.

• Polymeric phases (25�m or greater thickness): Here a di- or trichlorosilane isused in the presence of water vapour which provokes a polymerization of thereactant in solution prior to deposit and bonding with the silica. A reticulatedpolymer layer is obtained. At the molecular scale the final framework of thecoating is difficult to imagine: it is mono- or multilayer.

Modification of the silica surface

Si–OH

Si–O–SiMe2R

Si–O–SiMe2R

Si–O–Si–O–Si...

R R

MeMe SiO

SiO

SiO

SiO

SiO

SiO

OSiMe2R

OSiMe2OR

O OH OSi

O

OH

RMe

Me

Me

Si–O–Si–-R

Me

Me

Si–O–Si–

Me

Me

Me+ –

Me

Monomeric layer

Si–OH

Si–OH

Si–OH

Si–OH

Si–OH

Si–OH

Polymeric layer

CISiMe2R

CI2SiMeR

+ H2O

Si–O–Si–-R

CH2–CH2–N–CH2–CH2–CH2–SO3

R = C8H17 (RP-8)

R = C18H37 (RP-18)

Monomeric surfacemodification

Figure 3.10 Formation of bonded organosilanes at the interface of silica gel. Diagram of organicmonomers and polymers at the surface of silica gel. Close-up of a ‘long-haired’ particle withalkyl ligands. When hydrocarbons are bonded onto the silica, they orient themselves at theinterface in a particular manner according to their lipophilic and hydrophilic character againstthe mobile phase. The arrangement Si–O–Si–C is more stable than Si–O–C. For polymericcoatings, a carbon content exceeding 15 per cent can be attained on bonding to accessiblesilanol groups. Below, an example of a phase containing a zwitterion. Other reactions are alsoused (hydrosylylation in particular).

3.7 CHIRAL CHROMATOGRAPHY 75

3.6.3 Other stationary phases of varying polarity

The silica gels discussed previously contain bonded alkyl chains from 8 to 18carbon atoms. They are versatile and therefore very useful. Yet, for improving theseparation of certain classes of compound the tendency is now to use one of thegrowing number of specific stationary phases.

To the silica are bound linear chains bearing aminopropyl, cyanopropyl, benzylgroups or dipolar ligands (zwitterions) which confer an intermediate polarity tothe stationary phase (Figure 3.10). An improvement is noted in the separation ofvery small polar molecules which require mobile phases rich in water (cf. para-graph 3.8). For example, sugars, peptides and other hydrophilic compoundsbecome separable under these conditions (see, e.g. Figure 3.14). For these modifiedstationary phases, silica gel acts as a support.

Aluminium oxide �Al2O3� or zirconium oxide �ZrO2� are also used assupports of reticulated deposits based upon polymers of butadiene or styrene-divinylbenzene or hydroxymethylstyrene. Porous graphite, in the form of sphereswhose surface is 100 per cent carbon and therefore completely hydrophobic, hasbeen used in applications with compounds possessing atoms carrying lone pairsof electrons thus having high retention factors.

These stationary phases show a greater stability in both acidic and basic media,allowing certain columns to be rinsed with sodium hydroxide 1 M, that Si–O–Cbonds would not normally resist.

3.7 Chiral chromatography

A molecular organic compound whose structural formula reveals the presenceof an asymmetric centre leads generally to a mixture of two possible enan-tiomers R and S in variable quantities. If such a mixture is chromatographed ona column packed with a chiral stationary phase (a phase that contains active sitescorresponding to only one enantiomer, R for example), two peaks will be observedon the chromatogram (Figure 3.11). These peaks result from the reversible inter-actions R(compound)/R(stationary phase) and S(compound)/R(stationary phase)of which the stabilities are slightly different. The areas under the peaks are propor-tional to the abundance of each of the forms, R and S.

Among the general types of chiral stationary phase in current use in LC, are silicamatrix bonded to cyclodextrins via a small hydrocarbon chain linker (Figure 3.11).These cylindrically shaped ligands, which are oligosaccharides made of five to sevenmolecules of glucose, possess a hydrophobic internal cavity while the externalpart is hydrophilic. This gives them a selective permeability to a broad varietyof compounds leading ultimately to the formation of reversible diastereoisomercomplexes at the surface.


β-cyclodextrin

O O

O

OO

O

OO

O

O

OOH

HO

HO

HOHO

HO

HOHO

HO

HO

HO

HO

HO

OH

OH

OH

O

OH

O

OH

OH

OH

OH

O

Surface of a silica particle

Separation of a racemic mixture

12 14 20 min16 18

DL

7111

Cyclobond III

CH2OH CH2OH CH2OH

O

O

O

OO

OHHO

OH

OH

OHOH

OHOH

OH

OH

OHOH

OH

OH OH

D,L-tryptophaneHN

C C

NH2

CO2H

H

H

H∗

Figure 3.11 Separation on a cyclodextrin-bound stationary phase. Above left, the chromatogramof a racemic mixture of a compound (adopted from an Alltech document). Above right,structural formula of a �-cyclodextrin. These non-reducing cyclic oligosaccharides takes theform of a toroid (diameter, 1.5 nm ; hydrophobic cavity, 0.8 nm ; height, 0.8 nm). The inside ofthe toroid is hydrophobic as a result of the electron-rich environment provided in large part bythe glycosidic oxygen atoms. Below, partial representation of a cyclodextrin bonded through alinker to a silica matrix. These stationary phases are prepared using similar techniques to thosefor making reverse phases.

The optical purity of an analyte defined in terms of its enantiomeric excess (e.e.),is calculated from the following expression where AR and AS represent the areasunder the two peaks corresponding to the two enantiomers.

optical purity �e�e�%� = 100�AR − AS�AR + AS

3.8 Mobile phases

The degree of interaction between the mobile phase and the stationary phasewhether normal or reversed, affects the retention time of the analytes. In principle,the polarity of the stationary phase can lead to the following situations:

• If the stationary phase is polar, then the technique is said to be normal phasechromatography and a less polar mobile phase is used.

• If the stationary phase is non-polar, or only weakly polar then the techniqueis called reversed phase chromatography (RP-HPLC) – or chromatography on

3.8 MOBILE PHASES 77

STRONG

STRONGWEAK

WEAK

Eluotropic force Viscosity of water/solvent mixtures

100%Water

100%Solvent (1, 2 or 3)

Acetonitrile

Methanol

Ethanol

1

2

3

Vis

cosi

ty (

cent

ipoi

ses)

Solvent

HexaneToluene

TrichloromethaneDichloromethane

EtherEthyl acetateAcetonitrileMethanol

Water

Phase ofnormal polarity

Phase ofreversed polarity

1

2

3

Figure 3.12 Elutropic force and viscosity of solvents used as mobile phases. By mixing severalsolvents the elutropic strength of the mobile phase can be adjusted. Noting that the viscosityand by consequence the pressure at the head of the column varies according to the compositionof the mobile phase.

a hydrophobic phase. A polar mobile phase is selected (most commonly waterwith a modifying solvent such as methanol or acetonitrile). By changing thecomposition of the mobile phase and therefore its polarity, this affects thedistribution coefficients K �CS/CM� therefore the retention factors k of theanalytes (Figure 3.12). The main difficulty for the chromatographer is, as afunction of the compounds to be separated, to make the best choice of mobilephase (Figure 3.13).

Bonded silica phases lead in general to a large loss in polarity. With a phase ofthis type, of which the surface functionality resembles a paraffin layer the order ofelution will be the opposite of that encountered with normal phases. With a polareluent, a polar compound migrates faster than an apolar compound. Under theseconditions hydrocarbons are strongly retained. However, the polar compoundsthemselves are fairly difficult to separate. To solve this an elution gradient mustbe used by reducing progressively the water concentration (polar) thus benefittingthe modifying solvent chosen (less polar). For example, the elution begins withan 80/20 per cent mixture water/acetonitrile and ends with the composition,40/60 per cent for water/acetonitrile. This is the domain of hydrophilic interactionchromatography (HIC).

Four different types of interaction are possible between solvent molecules andthe analyte:

• Dipolar interactions when analyte and solvent both possess dipole moments

• Dispersion due to the attraction between molecules in proximity

• Dielectrics, which favour the solubility of ionic species in polar solvents


Polarity of several compound families

Hydrocarbons

Alcohols

Phenols

Acids

Tertiary amines

C18 - C8

Nitrile (CN)

Amine (NH2)

Silica (SiO2...)

Phenyl ( - C6H5)

Diol

Primary amines

Secondary amines

Hydroxyacids

Aldehydes and Ketones

Polarity of several type of stationary phases

weakly polar compounds strongly polar compounds

Figure 3.13 Relative polarities of several organic compound families along with some principaltypes of stationary phase with ligands in current use.

• Hydrogen bonding between solvent and analyte when one corresponds to thatof a proton donor and the other a proton acceptor.

The separation of very polar compounds on stationary phases of type RP-18requires the use of a mobile phase rich in water. Under these conditions thestationary phase, which is hydrophobic becomes suddenly waterproof and thecapacity for separation weakens. For this reason phases presenting a residualpolarity are preferred in order to maintain the interaction between the analytesand the water of the mobile phase (Figure 3.14).

3.9 Paired-ion chromatography

Paired-ion chromatography (PIC) is a technique related to RP-HPLC that affordsan improvement in the separation of some highly polar compounds such as aminoacids and organic acids that do not adhere at all to the stationary phase if itis apolar (Figure 3.15). Thus this polar character must be reduced to increaseretention. To modify the ionic charge, the pH of the mobile phase can be changedbut if this is not sufficient then a strongly ionic reagent, called a ion pairing reagent,is added to the mobile phase. This is usually a compound with a carbon chain(weakly polar) possessing a functionality whose charge is opposite to the analyteto be separated (e.g. heptane sulfonic acid if the ionic solute is a base). This forms

3.9 PAIRED-ION CHROMATOGRAPHY 79

a ‘neutralized’ ion pair, a less polar species, fairly stable and lipophilic, whichwill initially stick to non polar stationary phase but can still be eluted, apparentlyby a type of ion-exchange mechanism. This principle permits the separation ofinorganic cations or anions upon an RP-phase.

Column : LUNA NH2Hexane/Ethanol 85:15UV 240 nm

1 23

4 5 67

1 Glucose2 Maltose3 Maltotriose4 Maltotetraose5 Maltopentose6 Maltohexaose7 Maltoheptaose

C6H12O6C12H22O11C18H32O16C24H42O11C30H52O26C36H62O31C42H72O36

Min0 2 4 51 3

Figure 3.14 The separation of sugars upon an ‘amino’ phase. The order of elution of 7 homol-ogous sugars indicates that the stationary phase is polar and that the elutropic force of themobile phase diminishes as the molecular mass increases.

797-

0088

797-

0090

(b)

Type RP-18 columnUV detection at 254 nm

(a)

AMP = Adenosine monophosphate (n = 1)ADP = Adenosine diphosphate (n = 2)ATP = Adenosine triphosphate (n = 3)O

N

N

N

N

CH2OPOH

OHOH

NH2

O

OH

n

AMP

AMPADP ADPATP

ATP

min 0 2 min 40 4 6 10 12

Mobile phase:A = 0.1 M K2HPO4,pH = 6B = MethanolElution increasing B(gradient elution)

Mobile phase:A = 0.1 M K2HPO4, pH = 6+ nBu4N, H2SO4 4 mMol.B = MethanolElution with A/B = 75/25.

2 8

Figure 3.15 The effect upon separation of ion pairing on a column of reversed polarity. (a) Thechromatogram of a mixture of three nucleotides displaying the ‘normal’ situation of an elution inorder of reducing polarity; (b) Alternately, in the reverse phase situation: adenosine triphosphateassociated with the ion tetrabutylammonium has become more lipophilic and is thereforeretained longer (reproduced courtesy of Alltech).


1 - Cytochrome C2 - Myoglobine3 - Ribonuclease4 - Lysozyme5 - Chymotrypsinogen A

Column HIC-Phenyl (type RP-18)Mobile phase:A = (NH4)2SO4 2M + KH2PO4 0.1 M pH 7B = KH2PO4 0.1 M – pH 7Gradient with increase of Bfrom 15 to 100% in 30 min.UV Detection (280 nm)

794-

0462

1

23

45

0 10 20 30 40 min

ProteinSilica gelparticle

Figure 3.16 Separation improvement due to the principle of hydrophobic interaction. The chro-matogram of a mixture of proteins of decreasing hydrophilicity obtained by gradually reducingthe saline concentration (reproduced courtesy of Supelco).

3.10 Hydrophobic interaction chromatography

Hydrophobic interaction chromatography (HIC), is principally employed for theseparation of bio-organic compounds such as water soluble proteins. This sepa-ration takes advantage of the hydrophobic differences among the compoundspresent in the sample. Using an apolar stationary phase the elution is begun underconditions of a high salt concentration (e.g. 2 M ammonium sulfate and 0.1 mmonosodium phosphate, at pH 7). Under these conditions the proteins attachthemselves by their hydrophobic domains to the stationary phase. Next, a reversesalt gradient is started to gradually reduce the saline concentration in order thatthe proteins return to the mobile phase (Figure 3.16). They are eluted in decreasingorder of their hydrophilicity.

� This operation is similar to a technique employed in organic chemistry: in a sepa-rating funnel, in order to extract a compound diluted in an aqueous medium with ether,brine is introduced to reduce the solubility of the compound in water and thereby tofacilitate its extraction.

3.11 Principal detectors

The object of chromatography is rarely to determine the global composition of asample, but rather to measure the concentration of a compound that is present,for which a particularly well-adapted detector must be chosen. The universal

3.11 PRINCIPAL DETECTORS 81

detector is not, therefore, totally indispensable for quantitative analysis. On thecontrary it can even be a handicap leading to crowded chromatograms which areindecipherable.

More than in GC, the relative areas of the peaks of a chromatogram oftendo not have anything to do with the molar or mass composition of the mixtureanalysed. However, the detector, irrespective of its nature, is required to unite anumber of fundamental properties. It should give, for each compound of interest,a response that is proportional to the instantaneous mass flow (indicated by itslinear dynamic range), be sensitive, have a small inertia, filter most backgroundnoise and be stable over time.

The most widely used detection methods are based upon the optical properties ofthe analytes: absorption, fluorescence and refractive index (see also ELSD detector,Section 7.4).

3.11.1 Spectrophotometric detectors

Detection is based upon the Lambert–Beer Law �A = lC� : The absorbance Aof the mobile phase is measured at the outlet of the column, at one or severalwavelengths in the UV or visible spectrum (cf. Chapter 9). The intensity ofthe absorption depends upon the molar absorption coefficient of the speciesdetected. It is essential that the mobile phase be transparent or possess only a verylittle absorption (Figure 3.17).

The area of a peak, without taking into account this specific parameter, rendersthe direct calculation of concentration unfeasible by a simple check of the chro-matogram. Spectrophotometric detectors are examples of selective detection. Forcompounds that do not possess a significant absorption spectrum it is possible toperform derivatization of the analytes prior to detection.

Source Monochromator Flow cell Detector

0

0.2

0.4

0.6

0.8

1

Abs.

180 200 220 240 260 280 300

Wavelengths (nm)

1

2

3 4

1

2

3

4

Acetonitrile

Hexane

Methanol

Tetrahydrofurane

Absorbance of a cell of thickness1 cm filled with pure solvent

Figure 3.17 Photometric detection at a single wavelength. Principle of a photometric detectoralong with the absorption spectra of several solvents used in liquid chromatography. Here thetransparence limit of a solvent corresponds to an absorbance of 0.2 for 1 cm of optical path inthe cell.


• Monochromatic detection. The basic model comprises a deuterium or mercuryvapour light source, a monochromator for isolating a narrow bandwidth(10 nm) or a characteristic spectral line (e.g. 254 nm if the source is a mercurylamp), a flow cell with a volume of a few �L (optical path of 0.1 to 1 cm)and a means of optical detection.

• Polychromatic detection. More advanced detectors are able either to changewavelength during the course of an analysis, to record the absorbance atseveral wavelengths quasi-simultaneously, or even to capture in a fraction ofa second, a whole range of wavelengths without interrupting the circulationin the column (Figures 3.18 to 3.20). The diode array detector (DAD) leadsnot only to a chromatogram but also provides spectral information whichcan be used to identify the separated compounds (Figure 3.19). This is calledspecific detection (cf. Chapter 9).

The successive spectra of the compounds eluted with the mobile phase arerecorded continuously and stored in the memory of the instrument, to be treatedlater using appropriate software. Often spectacular chromatograms can be obtained(Figure 3.20). The ability to record thousands of spectra during a single analysisincreases the potential of these detectors systems. A topographic representation ofthe separation can be conducted, A = f �t� (iso-absorption diagrams).

� The rapid development of biotechnologies, as in biochemistry, requires the analysisof amino acids (proteins hydrolysates); photometric detectors can be used with thecondition that prior to passage in the measuring cell a post-column reaction withninhydrin is carried out (cf. Chapter 8).

A B

Detection at λ1 λ

Detection at λ2

λ1 λλ2

Time

Abs

.A

bs.

Chromatograms

same mixture

tA tB

UV spectra of A and B

B

A

ε

214 nm

230 nm

245 nm

Figure 3.18 Chromatograms of a sample containing two compounds A and B, for which the UVspectra are different. According to the choice of detection wavelength, the chromatogram will nothave the same aspect. On the right the chromatograms represent a mixture of several pesticidesrecorded at three different wavelengths which illustrates this phenomenon. In quantitativeanalysis therefore the response factors of each of the compounds must be determined prior tothe analysis (cf. Quantitative analysis, Chapter 4).


Optical

path

Polychromatic UV sourceFlow cell

Photodiode arrayConcave grating

Figure 3.19 Optical schematic of the diode array detector. The flow cell is irradiated witha polychromatic UV/Vis light source. The light transmitted by the sample is dispersed by aconcave grating towards a detector which comprises a diode array. The number of diodes canattain several hundred, each one monitoring the mean absorption of a very narrow interval ofwavelengths (e.g. 1 nm).

Elution time (min)

Wav

elen

gth

(mm

)

Abs

orba

nce

230236

242248

254260

266272

278284

290296

302308

314320

326332

338344

3500.00 5.60 11.20 16.80 22.40 28.00

Figure 3.20 Three-dimensional representation, I = f��t�, of a chromatographic separationobtained by a rapid recording method (reproduced courtesy of TSP instruments).

3.11.2 Fluorescence detector

About 10 per cent of organic compounds are fluorescent, in that they havethe ability to re-emit part of the light absorbed from the excitation source


(cf. Chapter 11). The intensity of this fluorescence is proportional to theconcentration of the analyte, as long as this concentration is kept low. Appli-cation to LC chromatography gave rise to fluorescence detectors, very sensitiveand for this reason often used for trace analysis. Unfortunately, the response isonly linear over a relatively limited concentration range of two orders of magni-tude. The domain of this selective detector (Figure 3.21), can be extended bythe application of a derivatization procedure pre- or post-column to make the

HH

O

O

RNH2

OPA

N R

Excitationradiation(monochromatic)

A fluorescence flow cell

Microcell(7–8 µL)

1 -

2 - HS–(CH2)2–OH

S-(CH2)2-OH

1

2

3

4

5

6

7

8 9 10

1 - Dead time2 - Pyrene3 - Benz(a) anthracene4 - Chrysene5 - Benzo(b) fluoranthene6 - Benzo(k) fluoranthene7 - Benzo(a) pyrene8 - Dibenzo(a,h) anthracene9 - Benzo(g,h,i) perylene

10 - Indeno(1,2,3cd) pyrene

15 Min

Polycyclic aromatic hydrocarbons (PAH)

Fluorescence detectorExcitation 280 nmEmission > 390 nm

Column ChromSep DI 200 × 3mmMobile phase acetonitrile/water 78/22Flow rate 0.7 mL/min

Photo cell

MP inlet

MP outletFluorescentlight

UV source S

Figure 3.21 Flow-cell of a fluorometric detector. Above left, examples of reagents used to renderfluorescent compounds containing primary amines through the action o- phthalic acid (OPA)in the presence of monothioglycol. Above right, a flow cell made of Pyrex glass is used asthe sensor through which the excitation light (as UV at 254 nm produced by the mercurylamp) passes axially. A photocell is situated at the side of the cell to receive radially emittedlight (perpendicular to the direction of the primary light). Below, chromatogram of a mixtureof several polycyclic aromatic hydrocarbons (PAH). The intensity of the fluorescence variesfrom one compound to another because there are variations in fluorescent quantum yields. Toremedy this, the excitation wavelength should be adjusted for each compound. This is donewith programmable detectors, able to select the optimal technical conditions for each species.


substances of interest detectable. There are a number of reagents that have beendeveloped specifically to synthesized fluorescent derivatives. For this methodologyan automatic reagent dispenser is placed either prior to the column or betweenthe column and the detector to effect one, or several reactions, upon the sampleanalytes in order to render them fluorescent before or after injection.

� By following this principle, traces of carbamates (pesticides) in the environ-ment can be measured by saponification with sodium hydroxide and then reactionwith o-phthalic aldehyde to transform the methylamine into a fluorescing derivative(Figure 3.21).

3.11.3 Refractive index detector (RI detector)

This type of detector relies on the Fresnel principle of light transmission through atransparent medium of refractive index n. It is designed to measure continuouslythe difference in the refractive index between the mobile phase ahead of andfollowing the column. So a differential refractometer is used. Schematically, abeam of light travels through a cell that has two compartments: one is filled withthe pure mobile phase while the other is filled with the mobile phase eluting thecolumn (Figure 3.22). In practice, the optical dispersions of the media are likelyto differ, and consequently the refractive index will only match at one particularwavelength. As a result the fully transmitted light will be largely monochromatic.The change in refractive index between the two liquids, which appears when acompound is eluting the column, is visualized as an angular displacement of therefracted beam. In practice, the signal corresponds to a continuous measurementof the retroaction that must be provided to the optical element in order tocompensate the deviation of the refracted beam.

The refractive index detector is one of the least sensitive LC detectors. It isvery affected by changes in ambient temperature, in pressure and in flow-rate.The temperature of the detector must be regulated with precision (to 0�001�C)and the column thermostatically controlled. This detector leads to both positiveand negative peaks, which requires that the baseline is fixed at the mid-heightof the graph (Figure 3.22). Also, this detector can only be used in the isocraticmode because in gradient elution, the composition of the mobile phase evolveswith time, as does its refractive index. The compensation, easily obtained in thecase of a mobile phase of constant composition, is no longer attainable when thecomposition of the eluent at the outlet of the column differs from that at the inlet.Consequently, it is often arranged in series with other detectors, in the isocraticmode, to give a supplementary chromatogram.

Despite these disadvantages, this detector, considered to be almost universal, isextremely useful for detecting compounds that are non-ionic, do not adsorb inthe UV, and do not fluoresce. It finds use in the recognition of those substances(fatty acids, alcohols, sugars, etc.) that are not easily detected by other means.


Chromatogram

10 15 20 min

Dual area photodiode assembly

Impact of thetwo beams

Mobile phaseof reference

Refractometric flow cell (here n1 > n2)

Mobile phasedownstreamfrom column

Signal

DetectorSource Flow cell Opticalcompensator

Feedbackcontrol device

S

n1

n2

r

i

Sensor

Incident beam

Sample cell

deflected beam

Reference cell

Figure 3.22 Schematics of a differential refractive index detector. The measurement of refractiveindex in liquid chromatography detection systems can be done in a number of ways. Onthis schematic, as sample elutes through one side, the changing angle of refraction moves thebeam. This results in a change in the photon current falling on the dual stage photodiodewhich unbalances it. The responses of the two areas are maintained equal by the opticalassembly (not displayed). A chromatogram of a mixture of sugars obtained with this type ofdetector. A commercial instrument, the model Optilab rEX (reproduced courtesy of WyattTechnology).

3.11.4 Other detectors

As has already been explained for GC, the identification of a compound fromits retention time alone can be uncertain. A more useful detector installed at theoutlet of the column would be able to give complementary information about thecompound being eluted.

When the detector itself is providing a second analytical method of analysis,qualifying it as bi-dimensional, identification becomes more certain. These canbe a spectrophotometer used simultaneously as a classic detector (obtaining thechromatogram) and as an identification tool (obtaining the spectrum) for theseparated species (cf. section 16.5). Coupling an LC instrument with a mass

3.12 EVOLUTION AND APPLICATIONS OF HPLC 87

spectrometer (tandem HPLC-MS) is equally very useful for identifying mixturesof known substances when a database of compounds under investigation is avail-able. Coupling with a proton-NMR spectrometer (tandem HPLC-NMR 1H),now possible owing to the increasing sensitivities of modern instruments, facil-itates the study of mixtures comprising unknown compounds (cf. Chapters 15and 16).

3.12 Evolution and applications of HPLC

The success of the tandem HPLC-MS analytical method has enabled liquid chro-matography to progress toward miniaturization (Figure 3.23). In fact the principalproblem for a mass spectrometer installed at the outlet of a liquid chromatographis the elimination of the mobile phase. To deal with this, either capillary liquidchromatography, or nano-chromatography, two improvements of the technique,simplify the interfacing from one apparatus to the other, and allows to solve thisproblem.

The suitability of micro-columns to HPLC has been revealed by the improvedperformance of separation. Yet the passage of the technique into the kingdom ofLilliput was not carried out without difficulty. The micro-environment requiresunderstanding, from the micro-flow rates of the mobile phase to the smallestpossible void volumes, from the mixing chamber for gradients to the volumeof the detection cell. The micro-leaks from conventional pumps are roughly ofthe order of the flow rates attained in miniature. A customized chromatographmust be used or a conventional system must be adapted because the repro-ducibility of flow rate gradients is difficult at this scale. A split containing asecond packed column or a long capillary is generally used, which acts as arestrictor.

Apart from the reduction in the scale of the quantities separated, two otherareas of progression should be noted:

4.6 mm (inner diam.)

1:1 1:235 1:3762

1 mL/min(standard flow rate)

2 mm 0.3 mm 0.08 mm

1:5.3

0.2 mL/min 7 μL/min 0.3 μL/min

Figure 3.23 Comparison of flow rates in columns of different internal diameters. If the packingin these four columns is of a similar nature, there are advantages by passing from the classicHPLC (left) to the capillary or to the nano-HCLP (right). The narrower the column the greaterthe decrease in mobile phase consumption.


15 cm × 4.6 mm (ID) column 5 cm × 4.6 mm (ID) column

Min5 10 15 20 25 300 Min5 10 15 20 25 300

Column Hypersil, 1.9 μm, 20 mm × 2.1 mm.Flow-rate 0.5 mL/min; T = 30° C; MS DetectionMobile phase, water and acetonitrile, gradient elution.

1 - atenolol

Rel

ativ

e ab

unda

nce

2 - nadolol3 - pindolol4 - timolol5 - metoprolol6 - oxprenolol7 - propanolol

β-blockers

(a)

(b)

6 7

Column size21 × 2.1 mm

0 1 2 cm

0.0

0

20

30

40

50

60

70

80

0.1

Time (min)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

1

3

4

2

5

Figure 3.24 Fast chromatography. (A) Comparison of two chromatograms obtained from thesame compound mixture. The shorter column packed with smaller particles enables to save anappreciable lot of time for comparable performances. (B) Separation of seven �-blockers usinga short column and small particles. The seven compounds are separated in under one minute(reproduced courtesy of Thermo Electron Corporation).

1. The use of stationary phases adapted to particular separations: sugars, PAH,amines, nucleotides…

2. Studies to reduce the time of analysis while maintaining the quality of resolu-tion. To achieve this, short columns are used with stationary phases formedeither from non-porous particles of small diameter (3�m or less), or ofporous networks of silica gel (monolithic column). This allows faster flowrates, then more rapid separations (Figure 3.24). This technique is mostfrequently used in chemical industries, and areas as food processing, envi-ronment, pharmacy and biochemistry.

PROBLEMS 89

Problems

3.1 Current HPLC apparatus can use columns of internal diameter (written asID in the text), of 300�m, and for which the optimum flow rate advised is4�L/min.

1. Show by simple calculation that this flow rate will conduct the mobilephase at practically the same linear speed as in a column of the sametype but possessing a standard diameter of 4.6 mm for which the advisedflow rate is 1 mL/min.

The chromatogram below corresponds to an example of separationobtained with a narrow column of 300�m × 25 cm.

2. What is the dead volume of this column? (The arrow marked on thechromatogram indicates the hold-up time.)


3. What is the retention volume, expressed in ml, of the compound whichhas the greatest affinity for the stationary phase?

4. Calculate the efficiency of the column for this compound.

5. Calculate the retention factor of this compound on the column.

6. What is the likely nature of the stationary phase? State precisely thesuperficial structure of such a phase. (On the figure ACN representsacetonitrile.)

Two columns selected for an experiment are filled with the same stationaryphase. One column has an internal diameter of 4.6 mm, the other 300�m,while both have the same length and an equal rate of filling �VS/VM�. It isdecided to use them in succession with the same chromatograph and underidentical conditions with the flow rates as advised above. An equal amountof the same compound is injected into each of them in turn.

7. When passing from one column to the other, would a differencein the retention volumes (or elution volume) of the compound beexpected?

8. If the sensitivity of the detector has not been adjusted between the twoexperiments, will the intensity of the corresponding elution peaks bedifferent?

3.2 What is the order of elution of the following acids from an HPLC columnwhose stationary phase is of type C18 while the mobile phase is a formatebuffer C = 200mM of pH 9.

Mixture:

1. Linoleic acid CH3�CH2�4CH = CHCH2CH = CH�CH�7CO2H2. Arachidic acid CH3�CH2�18CO2H3. Oleic acid CH3�CH2�7CH = CH�CH2�7CO2H

3.3 Indicate for each of the chromatographic techniques below the term whichbest expresses the analyte interaction with the stationary phase

PROBLEMS 91

1. Reverse phase a. Molecular mass2. Gel permeation b. Hydrophilicity3. Ionic chromatography c. Hydrophobicity4. Normal phase d. Protonation/ionisation

3.4 Consider a study, by HPLC, of the separation of three nucleotides (AMP, ADPand ATP), with a column of type RP-18. The mobile phase is a binary mixtureof H2O − KH2PO4, 0.1 M (pH 6)/methanol (90/10). The compounds appearin the order ATP, ADP, AMP. If a solution of 4 mM tetrabutylammoniumhydrogen sulphate is added to the mobile phase, the order of elution of thesecompounds is reversed (see Figure 3.15).

Explain the reasons for this phenomenon.

3.5 The separation of two compounds A and B is studied by HPLC on a columnof type RP-18. The mobile phase is a binary mixture of water and acetonitrile.A linear relationship exists between the logarithm of the retention factor andthe % of acetonitrile within the binary mixture �H2O/CH3CN�.

Two chromatograms were obtained, one in which the mixture of waterand acetonitrile was 70/30 v/v, respectively and the other where the sametwo components were mixed 30/70 v/v. The graph below was constructedfrom the results. The equations of the straight lines are,

for compound A:

log kA = −6�075 × 10−3�%CH3CN� + 1�3283

and for compound B:

log kB = −0�0107�%CH3CN� + 1�5235

1. Find the composition of the binary phase which leads to the selectivityfactor = 1.

2. Suppose that for each compound the width at half height of the corre-sponding peak in the chromatogram is the same and the efficiency of thecolumn is not modified following the composition of the mobile phase.For which combination of the binary mixtures mentioned above is theresolution between the two peaks the best? Discuss the practicalities ofyour choice.

4Ion chromatography

Ion chromatography (IC) is a separation technique which shares numerouscommon features with HPLC, yet possesses sufficient novel aspects such as itsprinciple of separation or modes of detection, to make it the object of a separatestudy. IC is adapted to the separation of ions and polar compounds. The mobilephase is composed of an aqueous ionic medium and the stationary phase is anion-exchange resin. Besides the detection methods based on absorbance or fluores-cence, ion chromatography also uses electrochemical methods based on the ionicnature of the species to be separated. Its greatest utility is for analysis of anionsfor which there are no other rapid analytical methods. Yet current applicationsof IC are far broader than the analysis of simple ions by which the techniquefirst gained renown. The operating domain, comparable with that of capillaryelectrophoresis, concerns the separation of many kinds of inorganic or organicspecies such as amino acids, carbohydrates, nucleotides, proteins and peptides incomplex matrices.

This chapter will also review the main methods of quantitative analysis fromchromatographic data.

4.1 Basics of ion chromatography

This chromatographic technique is concerned with the separation of ions and polarcompounds. Stationary phases contain ionic sites that create dipolar interactionswith the analytes present in the sample. If a compound has a high charge density,it will be retained a longer time by the stationary phase. This exchange process ismuch slower when compared with those found in other types of chromatography.This mechanism may be associated, for molecular compounds, with those alreadydealt with by HPLC when equipped with RP-columns.

For HPLC, some columns contain ion exchange packings but they are usedin significantly different ways. They are not considered to be IC columns. Theyrequire concentrated buffers that cannot be suppressed and so are not compatiblewith conductivity detection. Applications with these columns use more traditionalHPLC detection methods (such as UV or fluorescence).


94 CHAPTER 4 – ION CHROMATOGRAPHY

Mobile phase(aqueous)

Suppressor

Pump(s) Injectorwith loop

Time

Chromatogram

IC directIC via suppressor

COLUMN

Conductivitydetector

sign

al

Figure 4.1 Schematic of an ion chromatograph instrument. The classic modular building designof liquid chromatography is seen here again, yet with the difference that the separation isgenerally performed isocratically. The configuration shows a ‘suppressor’ device installed afterthe column and in series with a conductivity detector. The suppressor serves to eliminate theions arising from the eluent to improve sensitivity.

Ion chromatography instruments have the same modules as those found inHPLC (Figure 4.1). They can exist as individual components or as in an integratedmodel. The pieces into contact with the mobile phase should be made of inertmaterials capable of withstanding the corrosiveness of acid or alkaline entities,which serve as eluents. The detection of ionic species present in the sample isdifficult because these analytes are in low concentrations in a mobile phase thatcontains high quantities of ions.

The separation of compounds within the sample is founded upon the occurrenceof ion exchange, for which two classic examples are given below:

• if cationic species (type M+) are to be separated, a cationic column witha stationary phase capable of exchanging cations will be employed. Such aphase is constituted, for example, of a polymer containing sulfonate �−SO−

3 �groups. Consequently the stationary phase is the equivalent of a polyanion.

• alternately, if anionic species (type A−) are to be separated, an anionic columnis selected capable of exchanging anions. This is achieved, for example, byemploying a polymer containing quaternary ammonium groups.

To understand the mechanism of a separation, take for example an anionic columncontaining quaternary ammonium groups, in equilibrium with a mobile phasecomposed of a solution of hydrogenated carbonate anions (e.g. sodium counterions). All of the cationic sites of the stationary phase find themselves paired withanions of the mobile phase (Figure 4.2).

When an anion A− within the sample is taken up by the mobile phase, a seriesof reversible equilibria are produced which are directed by an exchange equationgiving the ion’s distribution between the mobile phase (MP) and the stationaryphase (SP).

4.1 BASICS OF ION CHROMATOGRAPHY 95

1 2 3

E–E–

E–

N+E– E– E–

E–

E–

E–

E–

N+

N+N+ N+

N+

A–

A–

A–

Figure 4.2 Scheme showing the progression of an anion A− by successive exchanges with the counteranion E− in contact with an ammonium stationary phase. (1) Initially the counterion E− fixed to thestationary phase is exchanged with the anionic species A− present in the mobile phase. (2) Next, theelution inverses the phenomenon by regenerating the stationary phase with the anion E− which,(3) substitutes again for A− on the stationary phase. The ion OH− would be the simplest choicefor E− but mixtures of carbonate and of hydrogenocarbonate �CO2−

3 and HCO−3 at 0.003 M) are

preferred since they are more efficient to displace the anions to be separated.

Arrow 1 corresponds to the attachment of the anion A− to the SP and arrow2 to its return to the mobile phase and therefore to its progression down thecolumn.

A−MP+�HCO3�

−SP

1�

2�HCO3�

−MP + A−

SP

�A−SP� · ��HCO3�

−MP�

�A−MP� · ��HCO3�

−SP�

= Kequ (4.1)

Kequ represents the selectivity between the two anions with respect to the cationof the stationary phase. As different anions have different Kequ they are thereforeretained on the column during different times. The time at which a given ionelutes from the column can be controlled by adjusting the pH. Most of instru-ments use two mobile phase reservoirs containing buffers of different pH, and

min

0

0

10

30

40

50

60

20

2 4 6 8 10

Column: Universal Cation HR, 3 µm AlltechDetector: ConductivityMob. phase: 3 mMol/L Methanesulfonic acidl

1 - Lithium2 - Sodium3 - Ammonium4 - Potassium5 - Magnesium6 - Calcium

1

23

4 5

6µS/c

m

Figure 4.3 Separation of several cations, mono and divalents with a cationic column (Courtesyof Alltech)


a programmable pump that can change the pH of the mobile phase during theseparation.

Using a cation exchange resin, a similar situation can be described (the stationaryphase SP corresponds, for example, to Polym-SO3H, strongly acidic):

M+MP + H+

SP1�

2M+

SP + M+MP

This exchange phenomenon, which allows polar species to be retained on theresin, is known as solid phase extraction (Figure 4.3). If the sample contains twoions X and Y and if KY > KX, Y will be retained more than X on the column.


Ion chromatography can be subdivided into cation exchange chromatography, inwhich positively charged ions bind to a negatively charged stationary phase andanion exchange chromatography, in which the negatively charged ions bind toa positively charged stationary phase. The column packings consist of a reactivelayer bonded to inert polymeric particles. Stationary phases must satisfy implicitlya number of requirements as narrow granulometric distribution (mono-disperse),large specific surface area, mechanical resistance, stability under acid and basicpHs and rapid ion transfer.

4.2.1 Polymer-based materials

The best known stationary phases are issued from copolymers of styrene anddivinylbenzene, in order to obtain packings hard enough to resist pressure inthe column. They are made of spherical particles with diameters of 5 to 15�m(Figure 4.4) that are modified on the surface in order to introduce functionalgroups with acidic or basic properties.

For cation separation the cation-exchange resin is usually a sulfonic or carboxylicacid. Thus, concentrated sulfuric acid is used to attack the accessible aromaticrings of the copolymer surface to link SO3H functional groups. A strongly acidicphase is obtained – for cation exchange – on which the anion is fixed to themacromolecule while the cation can be reversibly exchanged with other cationicspecies present in the mobile phase. These materials are stable over a wide rangeof pHs and have an exchange capacity of a few mmol/g.

� Another approach for obtaining these stationary phases is based on the copolymer-ization of a mixture of two acrylic monomers. One is anionic (or cationic), accordingto the nature of the phase desired, and the other is polyhydroxylated (Figure 4.5), inorder to ensure the hydrophilic character of the stationary phase. There is, however,an inconvenience with these resins as their rate of swelling depends upon the


+++

+

+ +++

+

+

+

++

+

++

+

+

+

+

+

+

+ ++

+

+

+

+

+

+

+

++

+

+

+

+

+

+

+

+

+

+

+

++

+

Cation exchange resin Anion exchange resin(DEAE exchanger)

SO3–H+

n n

NH+ OH–

0.1 μm

CH2 CH2

CH2CH3

CH2CH3

Coreparticle5–15 μm

Figure 4.4 Stationary phases in IC. Cross-section of a spherical particle of polystyrene used asa cation exchanger. The polystyrene matrix is transformed either to a cation (ex. DOWEX® 4)or to an anion (ex. DOWEX® MSA-1) exchange resin. For anion separation the resin is usuallya quaternary ammonium group.

composition of the mobile phase. They are normally reserved for medium pressurechromatography and some biochemical applications.

Starting from the same copolymer, an anion exchange resin can be synthesized,first by chloromethylation, which binds−CH2Cl (Merryfield’s resin), followed byreaction with a secondary or tertiary amine depending on the basicity requiredfor the stationary phase.

On contact with water a mildly basic stationary phase such as Polym-NMe2

yields a weakly ionized phase (Polym-NMe2H�+OH− especially when the mediumis basic. Alternately in an acidic medium it will appear as a strongly basic phasewhose active surface will be strongly ionized: (Polym-NMe2H�+Cl−. The exchangecapacity of these resins varies with the pH.

4.2.2 Silica-based materials

Porous silica particles can serve to support, through covalent bonding, alkylphenylchains carrying sulfonated groups or quaternary ammonium groups. This fixationstep is similar to that used to obtain bonded silica phases developed in HPLC.

Me

HN OCO2H

C(CH2OH)3

n

Figure 4.5 Copolymerization of two monoethylenic monomers (an acid and a trihydroxyamide).Example of the structure obtained (CM-TRISACRYL M® of IBF-France). Arising from a weakacid the resultant phase will be unusable at acid pH, as it will no longer be in its ionized form.


Reactive surface

CoreIonic coating

CO2H

CO2H n

Coreparticle

Latex

Figure 4.6 Film resins. Example of a resin made from a hard core onto which has beendeposited a copolymer, derived from the reaction of maleic acid on 1,3-butadiene (Reproducedcourtesy of the Dionex Company).

Some of these phases associate the properties of ion chromatography with those ofHPLC. Separations depend simultaneously on both ionic coefficients and partitioncoefficients. Silica packings usually display greater efficiency than their polymericequivalents.

4.2.3 Resin films

A polymer called ‘latex’, prepared from a monomer that contains organic groups,is deposited as an array of tiny beads �0�1–0�2�m in diameter) on an waterproofsupport to form a continuous film-like layer about 1–2�m thickness. The supportis made of micro-spheres of silica or glass or polystyrene of about 25�m diameter(Figure 4.6) This gives rapid equilibriums between stationary and mobile phases.

Latex polymer results from the reaction of two unsaturated monomers such as1,3-butadiene with maleic acid or 2-hydroxyethyl methacrylate.

4.3 Mobile phases

IC mobile phases are usually 100 per cent aqueous with organic or inorganicbuffers to control selectivity and when necessary a small content of methanolor acetone used to dissolve certain samples having a low degree of ionization.Depending upon the type of stationary phase, the counter ions present in themobile phase derived from acids (perchloric, benzoic, phthalic, methane sulfonic),or bases (the most popular for anion analyses are variants of sodium hydroxideand sodium carbonate/bicarbonate).

The pH is adjusted according to the separation to be achieved. The eluentscan be prepared in advance remembering that basic solutions have a tendency toabsorb atmospheric carbon dioxide, with for consequence a modification in theretention times.

4.3 MOBILE PHASES 99

–

+

H2O pure H2O + KOH (pure, without CO2)

Detail of the electrolytic OH - generating cell

Electrolyte reservoir(KOH solution)

Membrane, cationsexchanger

Pt cathode

Pt anode

K+ 2 H2O + 2e–

H2O – 2e–

Oxidation at the anode

Reduction at the cathode

2H+ + 1/2 O2

2OH– + H2

Pump Ionchromatograph

Degasser

Degasser

Electrical supply–+

O2 to the anode

H2 to the cathodeH2O

Electrolyticgenerator (KOH)

KOH

Figure 4.7 Ion chromatograph containing a high-purity OH− generator. Schematic showingthe position of the generator between pump and chromatograph. The degasser facilitates theelimination of gas which forms around the electrode located in the eluent stream. A K+ ion isformed for every OH− generated. Isocratic or gradient elution is provided on demand (diagrambased on a document from Dionex).

To avoid these inconveniences, an eluent generator can be used (either acidicor basic) which is inserted, as a supplementary module, between the pump andthe injector of the ion chromatograph (Figure 4.7). If the flow rate of water andthe electrolytic current are known then the concentration of the eluent can bedetermined with precision and concentration gradients can be effected, a procedureseldom used in ion chromatography.Injection peak. The first peak in a chromatogram for anions results from the ionicstrength of the injected sample being different than that of the eluent. The anionsin the sample displace the anions (e.g. carbonate/bicarbonate or hydroxide) thatare adsorbed onto the column packing. These displaced anions move forwardswith the mobile phase and when passed through the detector appear as a positivepeak (Figure 4.8). If a suppressor (cf. section 4.5) is installed at the column outletand if carbonates make the mobile phase, a negative peak, called the ‘water dip’is often present. This peak is the result of carbon dioxide which is formed in thesuppressed mobile phase (in the form of carbonic acid).

If the ionic strength of the sample is greater than that of the eluent, there willbe a positive peak. These peaks indicate the hold-up time of the chromatogramunderway.


0 3 6 9 12 15 min

Eluting anions Eluting anions

Water dip

Column: Allsep AnionDetector: Suppressed ConductivityMob. phase: 0.85 mM NaHCO3

1 : Borate2 : Silicate3 : Formate4 : Sulfide5 : Chloride6 : Cyanide

1: Iodate2: Bromate

1

2

0 4 6 min

1

23

4 5 6

Injection peak

Column: Anion/RDetector: ConductivityMob. phase: 5 mM p-HO-benzoic acid, pH 8.5

Figure 4.8 Chromatograms displaying injection peak. The injection peak is the unretained peakthat allows access to retention factors. This is normally the first peak on the chromatogram. Itcan interfere with other early-eluting anions such as fluoride (Chromatograms from Alltech).

4.4 Conductivity detectors

Besides the spectrophotometric detectors based on absorbance or fluorescence ofUV/visible radiation, and used when the mobile phase does not absorb appreciably,another mode of detection exists based upon electrolyte conductivity. Thus, at theoutlet of the column, the conductance (the inverse of the resistance) of the mobilephase is measured between two microelectrodes. The measuring cell should be of avery small volume (approx. 2�L). The difficulty is to recognize in the total signalthe part due to ions or ionic substances present in the sample. In order to do directmeasurements, the ionic charge of the mobile phase has to be as low as possible andthe measuring cell requires strict temperature control to within 0�01 �C becauseof the high dependence of conductance on temperature �∼ 5%/�C).

The sensitivity of the detector to an ion X (valency z and molecular concen-tration C) can be predicted if its equivalent conductance �X� and that of theeluent ion E �E� are known. This depends from the difference K betweenthe equivalent conductances of ion X and that of E. K can be calculatedaccording to expression 4.2, knowing that the peak will be either positive ornegative.

K = C�X − E� (4.2)

� The conductance G = 1/R that corresponds to the reciprocal of the resistance R,is measured between two electrodes which are plunged into the conducting solutionand across which is maintained a potential difference. G is expressed in Siemens (S).For a given ion, the conductance of the solution varies with the concentration of the

4.5 ION SUPPRESSORS 101

electrolyte. This relationship is linear for very dilute solutions. The specific conduc-tance (in S/mol) or conductivity k, permits the measure to be independent of thedetection cell parameters:

k = GKcell (4.3)

Kcell = d/A represents the cell constant (area A and spacing d). Its value cannotbe obtained by direct measurement, but is determined from a standard solution forwhich the conductivity k is known.

Finally the equivalent ionic conductance (S·m2/mol) represents the conductivity ofan ion with a valence z, in an aqueous solution at 25 �C, when the molar concentrationC (mol/L) tends towards zero in water (Table 4.1).

0 = 1000k/Cz (4.4)

Table 4.1 Equivalent ionic conductivities of ions at infinite dilution in water at 25 �C

Cations +0 �S · m2/mol� × 10−4 Anions −

0 �S · m2/mol� × 10−4

H+ 350∗ OH− 198Na+ 50 F− 54K+ 74 Cl− 76NH+

4 73 HCO−3 45

1/2Ca2+ 60 H2PO−4 33

∗ 3 500 000 S · m2/mol or 350 in S · cm2/mol ·

4.5 Ion suppressors

The mobile phase contains ions that create a background conductivity, making itdifficult to measure the conductivity due only to the analyte ions as they exit thecolumn. To improve the signal to noise ratio, when using a conductivity detector,a device called a suppressor, designed to selectively remove the mobile phase ions isplaced after the analytical column and before the detector. The principle consiststo convert the mobile phase ions to a neutral form or replacing them by others ofhigher conductivity. Suppressor-based detection is more useful for anion analysisthan for cation analysis.

The simplest model of a suppressor can be considered as a column whichcontains a stationary phase having functional groups of opposing charge to thoseof the separating column. Such a chemical suppressor, which contains an anionicresin is associated to a cationic separation column. The mechanism of action canbe described using the following example.

Suppose that a mixture containing the cations Na+ and K+ has been separatedusing a cationic column whose mobile phase contains dilute hydrochloric acid.In this acidic medium, at the outlet of the column, the Na+ and the K+ ions


are accompanied by H+ ions coming from the acid and Cl− anions in orderto assure the electroneutrality of the medium. After the separation column, themobile phase flows through a second column which contains an anionic exchangeresin whose mobile ion is OH−. The Cl− anions will be affixed on this column,thus displacing the OH− ions that will react with H+ ions in solution to givewater. At the outlet of the suppressor, only �Na+OH−� and �K+OH−� species arefound in water. The ions H+ and Cl− have effectively disappeared. As OH− has ahigher conductivity than Cl−, detection of the Na+ and K+ ions is easier, becauseamplified (Figure 4.9).

In summary, for anion analyses (using a conductivity detector), ion suppres-sors neutralize the mobile phase, reducing its conductivity, while simultaneouslyincreasing the sample’s conductivity.

The limitation of this type of suppressor lies in its very large dead volume thatreduces the separation efficiency, due to a remixing of the ions prior to theirdetection. The ions of the suppressor should be regenerated periodically and itshould be used exclusively in the isocratic mode.

Other types of suppressors, having a high ionic capacity, have subsequently beendeveloped. They are made of porous fibres or of micromembranes and possessvery small dead volumes in the order of 30–50�L. That allows gradient elutionwith a negligible baseline drift. Figure 4.10(a) shows the passage of an anion A−,in solution in a typical electrolyte used for anionic columns, through a suppressorwith a cationic membrane.

Nowadays, continuous regenerated suppressors which make use of electrolyticreactions have been introduced for traces determinations. They behave either

Elution of the cation M+

Chemical suppressor

H2O H2O

Cl– + +OH–R4N+OH– R4N+Cl–

Anion exchange packing Conductivity detectorSeparating column

Ions before suppressor Ions after suppressor

Cl–H+ OH–M+ M+

Figure 4.9 Chemical suppressor for an exchange cation column. For cation analysis, the mobilephase is often dilutes HCl or HNO3 solutions, which can be neutralized by an eluent suppressorthat supplies OH−. In this example the anionic suppressor purges the mobile phase of H+ ionsand of almost all of the Cl− ions, facilitating the detection of the cation M+. The same principleholds for anion analysis. In this case, the mobile phase is often dilute NaOH or NaHCO3, andthe eluent suppressor supplies H+ to neutralize the anion and retain or remove the Na+.

4.5 ION SUPPRESSORS 103

Chromatogram

1 2

3

4

5

6

7

8

++

++

++

++

++

++

+

+

+

Suppressor

Separation column

Elution of anion A–

(a) Porous membrane suppressor installed at the outlet of an anionic separating column

Elution of cation M+

SO4

– –SO4

– –

H2O

H2O

H2O

H2O

H2O

H2O

H2O H2O

H2OA–

A–

H2CO3

H2CO3

H2SO4

H2SO4

Na2SO4

HCO3

– + H

+

Na+

H+

M+

M+

H+

OH–

OH–

H+ +

OH–

Na+

+A

–

HCO3

–Na

+

Na+

towards the detector

towards the detector

Membrane permeableto cations

Cl–

Cl–

Cl–

Cl–

M+

H+

H+

H+

anod

e

cath

ode

(& O2) (& H2)

(b) Suppressor with auto-regenerating membrane installed at the outlet of a cationic column

Column IonPac (Dionex DX)Conductivity detectionEluent: 1.8 mM Na2CO3/1.7 mM NaHCO3flow: 1mL/min

5 - nitrate6 - phosphate7 - sulfate8 - oxalate

1 - fluoride2 - chloride3 - nitrite4 - bromide

0 – 10 min.

(c) Separation of anions

μS

0

10

+

Membrane permeableto anions

Figure 4.10 Membrane and electrochemically regenerated suppressors. There are two types ofmembranes, one type permeable to cations (H+ and in this example Na+), the other perme-able to anions (OH− and here Cl−). (a) The microporous cationic membrane is adapted tothe elution of anions. Only cations can cross the membrane (corresponding to a polyanionicwall which keeps away the anions in the solution). (b) An anionic membrane suppressorplaced, contrary to the preceding model, at the outlet of a cationic column. Ions are regen-erated by the electrolysis of water. Note in both cases the counter flow circulation betweenthe eluted phase and the solution of the post-column suppressor. (c) An example of a sepa-ration of inorganic cations (concentrations of the order of ppm) using a suppressor of thistype.


like a special column containing a resin which regenerates by electrolysis or likea membrane suppressor where the regenerating ions are produced in situ byelectrolysis of water. Figure 4.10b illustrates the second procedure: it represents thepassage of a cation, in a dilute hydrochloric acid solution, through a suppressorwhose membrane is permeable to anions.

Alternately, if the problem consists in the separation of a mixture of anions onan anionic column (cationic material), with an eluent containing dilute sodiumhydroxide, a membrane allowing the diffusion of cations will be chosen. At thecathode, the passage of hydronium ions towards the main flow of electrolyte willneutralize OH− ions. At the anode, Na+ ions will migrate out of the mobile phaseand will react with OH− ions.

Quantitative analysis by chromatography

The significant development of chromatography in quantitative analysis is essentiallydue to its reliability and its use in standardized analyses. Trace and ultratraceanalyses by chromatography are used, particularly the EPA methods for environmentalanalysis, although their costs are rather high. This type of analysis relies mainly onreproducibility of the separation and on the linear relationship between the injectedmass of a compound onto the column and the area of the corresponding peak onthe resultant chromatogram. This is an excellent comparative method used in manyprotocols, which, allied with software used for data treatment allow automation ofall the calculations associated with these analyses.

The three most widely used methods are described below accompanied in theirsimplest formats.

4.6 Principle and basic relationship

In order to calculate the mass concentration of a compound appearing as a peakon a chromatogram, two basic conditions must be met. First, an authentic sampleof the compound to be measured should be available, as a reference, to determinethe detector sensitivity to this compound. Second, a software giving the heightsor areas of the different eluting peaks of interest is also required. All of thequantitative methods in chromatography rely on these two principles. They arecomparative but not absolute methods.

For a given tuning of the instrument, it is assumed that a linear relation existsfor each peak of the chromatogram, over the entire concentration range, betweenits area and the quantity of the compound responsible for this peak in the injectedsample. This applies for a given concentration range depending on the detectoremployed. This hypothesis is translated into the following equation:

mi = Ki · Ai (4.5)

4.8 EXTERNAL STANDARD METHOD 105

where mi is mass of the compound i injected on the column, Ki is the abso-lute response factor for compound i and Ai is the area of the eluting peak forcompound i.

The absolute response factor Ki (not to be confused with the partition coeffi-cient), is not an intrinsic parameter of the compound since it depends upon thetuning of the chromatograph. To calculate the response factor Ki, according toexpression 4.5, it is essential that both the area Ai and the mass mi, of compoundi injected on the column, are known. However, this mass is difficult to determinewith precision since it relies simultaneously upon the syringe, upon the injectortype (in GC), or upon the injection loop (in HPLC). This is why most chromato-graphic methods utilized for quantitative analyses, whether pre-programmed intoan integrated recorder or in the multiplicity of available software, do not makeuse of the absolute response factors, Ki.

4.7 Areas of the peaks and data treatment software

To determine the areas of the peaks appropriate chromatographic software isused which also ensures not only the control and working of the chromatographbut also the data treatment to furnish a report corresponding to one of thepre-programmed methods of quantitative analysis.

The signal recovered by the detector is sampled by the analogue–digital converter(ADC) with a frequency of a few hundreds hertz in order to yield an accuratereproduction of the narrowest peaks in chromatograms obtained from GC withcapillary columns. Each software package allows baseline correction, treatmentof negative signals and all incorporate different methods to calculate peak areas(Figure 4.11).

� The manual triangulation method and the ‘cut and weight’ method (weight isconsidered proportional to area) are, of course, no longer employed. However it isuseful to remember that for a gaussian eluting peak, the product of its width at halfheight by its full height, corresponds to approximately 94 per cent of the total area ofthe peak. In the same way, recorders with an integration system for measuring thepeak areas are no longer used.

4.8 External standard method

This method allows the measurement of the concentration (or percentage in mass)of one or more components that appear as resolved peaks on the chromatogram,even in the presence of other compounds yielding unresolved peaks. Easy touse, this method corresponds to the application of a principle common to manyquantitative analysis techniques.

The modus operandi is based upon the comparison of two chromatogramsobtained successively without changing the control settings of the chromatograph


Figure 4.11 Quantitative analysis software for chromatography. Since the signal from thedetector situated at the outlet of the column is analogical, an analogue–digital converter (ADC)is necessary. The stored chromatogram, digitized, serves as a basis for its exploitation by thesoftware. Different zones of the screen can display the calibration curve, methodology, etc.(software Chemstation from Agilent Technologies).

(Figure 4.12). The first chromatogram is acquired from a standard solution(reference solution) of known concentration Cref in a solvent. The standard andsample matrix should be as similar as possible. A volume V of this solution isinjected. Analysis conditions must be identical. On the resulting chromatogram thearea Aref of the corresponding peak is measured. The second chromatogram resultsfrom the injection of the same volume V of the sample in solution, containingan unknown concentration of the compound to be measured (conc. Cunk�. Thearea of the corresponding peak is Aunk. Since an identical volume of both sampleshas been injected, the ratio of the areas is proportional to the ratio of concen-trations which depend upon the masses injected �mi = Ci · V �. Applied to thetwo chromatograms, expression 4.5 leads to relation 4.6, which characterizes thismethod:

mref = Cref · V = K · Aref and msam = Cunk · V = K · Aunk

Cunk = Cref

Aunk

Aref

(4.6)

4.9 INTERNAL STANDARD METHOD 107

Chromatogram of the standard (Cref)(reference solution)

Sol

vent

pea

k

Sol

vent

pea

k

Aunk·Aref.

Chromatogram of the solution (Cunk·)to be measured

0 0

Figure 4.12 Analysis by the external standard method. The precision of this basic methodis improved when several solutions of varying concentrations are used in order to create acalibration curve. For trace analyses by liquid chromatography it is sometimes advisable toreplace the areas of the peaks by their heights as they are less sensitive to variations in themobile phase flow rate.

The single point calibration method, as depicted in Figure 4.12, assumes thatthe calibration line goes through the origin. Precision will be improved if theconcentrations of the reference solution and of the sample solution are similar.

This technique, employing the absolute response factors, yields very reliableresults with chromatographs equipped with an auto-sampler: a combination ofa carousel sample holder and an automatic injector. This permits numerousmeasurements to be made without interruption, to the condition that no changein the apparatus tuning is made between injections.

The reference solution periodically injected affords a control that can be used tocompensate an eventual baseline drift during a sequence of programmed injections.

Precision can be also improved if several injections of the sample and the refer-ence solutions are made, always using equal volumes. In a multilevel calibration,equal volumes of a series of standard solutions are injected. This allows to geta calibration curve of A = f �C�, obtained by a regression method (linear least-square or quadratic least-square). This leads to a more precise value for Cunk

(Figure 4.11).This method, the only one adapted to gas samples, has the added advantage that

nothing needs to be added to the sample solution, unlike the method describedbelow.

4.9 Internal standard method

For trace analysis it is preferable to use a method that relies on the relativeresponse factor of each compound to be measured against a marker introducedas a reference. This means that any imprecision concerning the injected volumes,the principal constraint of the previous method, is compensated. As above, this


Sol

vent

pea

k

Sol

vent

pea

k

Chromatogram of the standards Chromatogram of the solution to be measured

11

ISIS

2

2

00

(IS = Internal Standard)A ′1 C ′1?C ′2?C ′IS

A ′2A ′IS

A1 C1C2CIS

A2AIS

Figure 4.13 Simple example illustrating the internal standard method

more reliable method requires two chromatograms, one to calculate the relativeresponse factors of the compounds of interest, and the other to analyse the sample.

The areas of the peaks to be quantified are compared with that of an internalstandard (designated by IS), introduced at a known concentration within thesample solution.

Supposing that a sample contains two compounds 1 and 2 to be measured andthat compound (IS) represents the additional compound for use as an internalstandard (Figure 4.13).

4.9.1 Calculation of the relative response factors

A solution containing compound 1 at known concentration C1, compound 2 atknown concentration C2 and the internal standard IS at known concentration CIS

is prepared then injected onto the chromatograph. A1, A2, AIS will be the areasof the elution peaks in the chromatogram due to the three compounds. If m1, m2

and mIS represent the real quantities introduced onto the column, of these threesubstances, then three relations of type 4.5 can be derived:

m1 = K1 · A1

m2 = K2 · A2

mIS = KIS · AIS

m1

mIS

= K1 · A1

KIS · AIS

andm2

mIS

= K2 · A2

KIS · AIS

These ratios enable the calculation of the relative response factors of 1 and 2, againstIS and designated by K1/IS and K2/IS:

K1/IS = K1

KIS

= m1 · AIS

mIS · A1

and K2/IS = K2

KIS

= m2 · AIS

mIS · A2

4.9 INTERNAL STANDARD METHOD 109

Since the injected masses mi are proportional to the corresponding mass concen-trations Ci�mi = CiV�, the above equations can be rewritten as follows:

K1/IS = C1 · AIS

CIS · A1

and K2/IS = C2 · AIS

CIS · A2

4.9.2 Chromatogram of the sample – calculation of theconcentrations

The second step of the analysis is to obtain a chromatogram for a given volumeof a solution containing the sample to quantify and to which has been added aknown quantity of internal standard IS. This will yield A′

1, A′2 and A′

IS the areasof this new chromatogram being obtained under the same operating conditionsas previously. If m′

1, m′2 and m′

IS represent the quantities of 1, 2 and IS introducedinto the column, then:

m′1

m′IS

= K1/IS · A′1

A′IS

andm′

2

m′IS

= K2/IS · A′2

A′IS

From the relative response factors calculated in the first experiment as well asfrom the known concentration of the internal standard within the sample, C ′

IS,this leads to :

C ′1 = C ′

ISK1/IS · A′1

A′IS

and C ′2 = C ′

ISK2/IS · A′2

A′IS

Expanding to n components it is easy to calculate the mass concentration of thesolute i using equation 4.7:

C ′i = C ′

ISKi/IS · A′i

A′IS

(4.7)

equally the percentage concentration of i can be expressed using equation 4.8:

Xi% = �C ′i/Mass of sample taken� × 100 (4.8)

This method becomes even more precise if several injections of the solution andof the sample are carried out. Often a same volume of an IS stock solution is spikedwith all standards and samples.

In conclusion, this general and reproducible method demands nevertheless agood choice of internal standard, which should have the following characteristics:

• it must be stable, pure and not exist in the initial sample


• it must be measurable, giving an elution peak well resolved on the chro-matogram

• its retention time must be close to that (or those) of the solute(s) to bequantified

• its concentration must be close to, or above that of the analytes to quantifyto gain a linear response from the detector

• it must not interfere and co-elute with a sample component.

4.10 Internal normalization method

This method, also called ‘normalized to 100 per cent’ is used for mixtures forwhich each component is producing a peak on the chromatogram, in order to beable to make a complete assessment of the sample concerned. The solvent, if any,is typically ignored.

Supposing that it is required to find the mass concentrations of three compounds1, 2, 3 in a mixture (Figure 4.14). The analysis is again carried out in two steps.

4.10.1 Calculation of the relative response factors

A standard solution containing the three compounds 1, 2, and 3 at known concen-trations C1, C2 and C3 is prepared. The chromatogram corresponding to theinjection of a volume V of this standard solution shows three peaks of area A1, A2

and A3. These areas will be related to the masses m1, m2 and m3 of the compoundsin volume V , by three expressions of type 4.5.

One of the compounds, 3 for example, is chosen as the substance for internalnormalization. This compound 3 will serve to calculate the relative response factorsK1/3 and K2/3 for compounds 1 and 2 with respect to 3. As previously deduced:

Chromatogram of the standard solution Chromatogram of sample solution

1

1

2

33

Cref.

Sol

vent

pea

k

Sol

vent

pea

k

0 0

Astandard

C3

C2

C1

A3

A2

A1

2

A′1A′2A′3

Cunk.Aunk.

C′1?C′2?C′3?

Figure 4.14 Analysis by internal normalization method. This method is commonly reported asthe default for early integrators

4.10 INTERNAL NORMALIZATION METHOD 111

K1/3 = K1

K3

= m1 · A3

m3 · A1

and K2/3 = K2

K3

= m2 · A3

m3 · A2

Given that mi =Ci�V , then the following expressions for K1/3 and K2/3 are obtained:

K1/3 = C1 · A3

C3 · A1

and K2/3 = C2 · A3

C3 · A2

4.10.2 Chromatogram of the sample – calculation of theconcentrations

The next step consists to inject a sample of the mixture to be measured containing1, 2 and 3. Labelling the elution peaks as A′

1, A′2 and A′

3 will gain direct access tothe percentage mass composition of the mixture represented by x1, x2 and x3 viathree expressions of the following form:

xi% = Ki/3 · A′i

K1/3 · A′1 + K2/3 · A′

2 + A′3

× 100 with i = 1 or 2 or 3� (4.9)

The condition of normalization being that: x1 + x2 + x3 = 100If the procedure is extrapolated to n components normalized to the component

j, a general expression for the response factor of a given compound i can beobtained (equation 4.10).

Ki/j = Ci · Aj

Cj · Ai

(4.10)

It is also possible to determine Ki/j by plotting a concentration-response curvefor each of the solutes.

In a mixture containing n components, if A′i designates the area of the elution

peak of compound i, and if the internal reference is j, then the content ofcompound i will obey the following equation 4.11:

xi% = Ki/j · A′i

n∑i=1

Ki/j · A′1

× 100 (4.11)

Supposing that detector gives responses that are independent from the substance(i.e. relative response factors identical as for a TCD detector in GC), this methodserves to give an estimation of relative concentrations. This was commonlyreported as the default for early integrators (equation 4.12).

xi% = A′i

n∑i=1

A′i

× 100 (4.12)


Problems

4.1 0.604 g of an undiluted stationary phase, comprising SO3H groups is intro-duced to an erlenmeyer. 100 mL of distilled water, is added and approximately2 g of NaCl. The liberated acidity is measured by sodium hydroxide 0.105 Min the presence of helianthin (methyl orange), as an indicator to identify theequivalence point (towards pH 4). If it is known that 25.4 mL of the sodiumhydroxide solution must be added to neutralise the acid liberated by thestationary phase, calculate its molar capacity in grams.

4.2 A mixture of proteins is separated on a column with a stationary phase ofcarboxymethylated cellulose. The internal diameter of the column is 0.75 cmand its length is 20 cm. The dead volume is 3 mL. The flow rate of the mobilephase is 1 mL/min. The pH of the mobile phase is adjusted to 4.8. Threepeaks appear upon the chromatogram corresponding to the elution volumesV1, V2 and V3 at 12 mL, 18 mL and 34 mL respectively.

1. Does this arise from an anionic or cationic phase? Give reasons for youranswer.

2. Why, when increasing the pH of the mobile phase, are the timesof elution of the three compounds subject to modification? Predictwhether these times are increased or decreased.

4.3 In measuring cyclosporin A (a treatment for skin and organ transplantrejection) by HPLC, according to a method derived from that of internalstandard, the following procedure is employed.

Preparation of the samples: An extraction of 1 mL of blood plasma ismade, to which is added 2 mL of a mixture of water, and acetonitrile (80/20),containing 250 ng of cyclosporin D as internal standard, which has a similarstructure to cyclosporin A.

The 3 mL of new mixture is now passed on a disposable solid phaseextraction column in order to separate the cyclosporins retained upon thesorbent. Following the rinsing and drying of the column, the cyclosporinsare eluted with 1.5 mL of acetonitrile and are then concentrated to 200�Lfollowing evaporation of solvent. A fraction of this final solution is injectedinto the chromatograph.

1. What is the concentration factor of the original plasma following thistreatment?

PROBLEMS 113

2. Can the rate of recuperation following the extraction step on the solidphase be deduced?

Sample: The standards are created with a plasma originally possessing nocyclosporin. Six different solutions are prepared by adding the necessaryquantities of cyclosporin A to each in order to create solutions of 50 ng/mL,100 ng/mL, 200 ng/mL, 400 ng/mL, 800 ng/mL, and 1000 ng/mL. 1 mL fromeach of these solutions is subjected to the same extraction sequence followingthe addition of 250 ng of cyclosporin D to each, as above.

ng/mL en cyclo. A 50 100 200 400 800 1000

Ratio of peaks heightscyclo.A/cyclo.D �Rh�

0.25 0.5 1.02 2.04 4.05 5.1

Column Supelco 75 × 4�6mm. Silica gel 3�m, phase RP-8.

3. Determine the concentration in units of ng/mL of cyclosporin A in theblood plasma giving rise to the chromatogram reproduced below. Thisquestion should be attempted in two ways:

a) By choosing a single point from a standard.

b) By using the gradient which it is possible to draw from the datain the table above (in both cases it will based upon the heights ofthe peaks).


4.4 The method of internal normalisation was chosen to determine the masscomposition of a sample comprising a mixture of four esters of butanoicacid. To this end, a reference solution containing known % masses of theseesters led to the following relative values of the response coefficients of thebutanoates of methyl (ME), of ethyl (EE), and of propyl (PE), all three inratio with butyl-butanoate (BE).

KME/BE = 0�919 KEE/BE = 0�913 KPE/BE = 1�06

From the chromatogram of the sample under analysis, reproduced below,and the information given in the table, find the mass composition of thismixture (ignore the first peak at 0.68 min.)

Peak no. tR compound Area (mV. min)

1 0�68 – 0�19002 2�54 methyl ester (ME) 2�34012 3�47 ethyl ester (EE) 2�35903 5�57 propyl ester (PE) 4�07735 7�34 butyl ester (BE) 4�3207

4.5 To measure serotonin (5-hydroxytryptamine), by the internal standardmethod, a 1 mL aliquot of the unknown solution is added to 1 mL of a solu-tion containing 30 ng of N-methyl-serotonin. This mixture is then treatedto remove all other compounds which could interfere with the experiment.

PROBLEMS 115

The operation performed was an extraction in the solid phase to isolate theserotonin and its methyl derivative, diluted in a suitable medium.

1. Why is the compound forming the internal standard added before theextraction step?

2. Calculate the response factor of the serotonin compared to that ofN-methyl-serotonin if it is known that the chromatogram yielded bythe standards gave the following results.

Name Area ��V�s� Quantity injected (ng)

Serotonin 30 885 982 5N-methyl-serotonin 30 956 727 5

3. From the chromatogram of the sample solution, find the concentrationof serotonin in the original sample, if it is known that:

— area serotonin 2573832�V/s— area N-methyl-serotonin 1719818�V/s

5Thin layer chromatography

Thin layer chromatography (TLC), also known as planar chromatography, isan invaluable method used in chemistry and biochemistry, complementary toHPLC while having its own specificity. Although these two methods are applieddifferently, the principle of separation and the nature of the phases remain thesame. Cheap and sensitive, this technique that is simple to use, can be automated. Ithas become essential principally since it is possible to undertake several separationsin parallel. The development of automatic applicators and densitometers haveled to nano-TLC, also called HPTLC, a highly sensitive technique which can behyphenated with mass spectrometry.

5.1 Principle of TLC

The principle of the separation between phases of the sample components issimilar to that of HPLC, though the migration of the constituents through thestationary phase is different. Separation is conducted on a thin layer �100–200�m�of stationary phase, usually based upon silica gel and deposited on a rectangularplate made out of glass, plastic or aluminium of a few centimetres in dimensions.To maintain the stationary phase on the support and to assure the cohesion ofthe particles, an inert binder like gypsum (or organic linker) is mixed into thestationary phase during the manufacture of the plate. The constituents can beidentified by simultaneously running standards with the unknown.

There are three steps to conduct a separation with this technique:

5.1.1 Deposition of the sample

A small volume of sample (between a few nanolitres to a few microlitres), dissolvedin a volatile solvent, is deposited close to the bottom of the plate as a small


118 CHAPTER 5 – THIN LAYER CHROMATOGRAPHY

Figure 5.1 Automatic sample deposition device for TLC and a system to ‘read’ the plate. Left,programmable applicator Linomat IV. Right, densitometer measuring the light either reflectedor transmitted by the plate. The optical set up is similar to that of a UV/visible spectrometer(model Scanner 3, reproduced courtesy of Camag).

spot of about 1–2 mm in diameter. This deposit is made either manually, orautomatically, with a flat ended capillary (Figure 5.1). The spot can also have theform of a horizontal band of a few millimetres which is obtained by automaticspraying of the sample. This last method has the advantage of having a highreproducibility, indispensable of course, for quantitative analysis. The preparedplate is then placed in a glass developing chamber that contains a small amount ofthe appropriate developing solvent. The chamber is then covered (Figure 5.2). Theposition at which the sample has been deposited must be above the level of thesolvent.

5.1.2 Developing the plate

The mobile phase rises up the stationary phase by capillarity, moving the compo-nents of the sample at various rates because of their different degrees of inter-action with the matrix and solubility in the solvent. Their separation maybe complete in a few minutes. When the solvent front has travelled a suffi-cient distance (several centimetres), the plate is withdrawn from the chamber,the position attained by the mobile phase is immediately noted then it isevaporated.

When using a plate of reversed polarity (‘RP-TLC’), the mobile phase willgenerally contain water. In this case it can be useful to add a salt such aslithium chloride which limits diffusion phenomena and thereby increases theresolution.

5.1 PRINCIPLE OF TLC 119

x0

x1

TLC plate

Eluent vapour

Eluent

Spot deposition

0.47

0.31

1

0

RfRf = x1/x0

Figure 5.2 Developing chamber and TLC plate. Left, available in a variety of dimensionsaccording to the size of the plates (of 5 × 5 to 20 × 20 cm), the chambers are made of glass andequipped with a tight fitting cover. Right, typical appearance after the TLC plate is partially dry.A faint line can be observed at the location of the solvent upper limit. This line is called thesolvent front. Calculation of Rf (cf. paragraph 5.4). A substance that does not migrate from thesample origin has a Rf = 0.

5.1.3 Identifying the spots

The localization of each component on the plate, which has now lost all of theeluent, consists to measure their migration distance from the original deposition.To locate colourless compounds the plate must be developed (Figure 5.2). In orderto facilitate the visualization of the spots,manufacturers sell plates that contain afluorescent salt of zinc which emits a bright green fluorescence when the plateis irradiated with a UV mercury vapour lamp �� = 254nm� and observed in aviewing cabinet. All compounds absorbing at this wavelength appear as a darkspot (or sometimes coloured) against a bright green blue background.

Another method to make compounds visible, almost universally used, consists ofheating the plate after spraying it with sulfuric acid which leaves charred blots behind.This approach is, however, not adapted to quantitative TLC; in this case, develop-ment is effected by immersion of the plate, using a general (phosphomolybdic acid,vanillin), or specific (e.g. ninhydrin in alcoholic solution for amino acids) reagent.Hundreds of reagents have been described that serve to introduce chromophores orfluorophores groups into the analytes molecules after separation.

The use of square TLC plates allows two-dimensional chromatography tobe carried out using two successive elutions with two different mobile phases(Figure 5.3). A high degree of separation can be achieved.


Sample deposition

Second elution

a a

a a

Limit of solvent migration

X

X

X

X

cba

(a) (b)

(c)(d)

Elution 1

Solvent 1First elution

cba

Elution 2

Solvent 2

cba

drying and 90° rotationof the plate

b c

cb b c

b c

Figure 5.3 Two-dimensional TLC. An experiment with separation processes using two differentsolvents performed in two perpendicular directions. (a) Deposition of an unknown X and threestandards; (b) migration in the first direction with the first solvent; (c) drying and rotationof the plate; (d) migration in the second direction with the second solvent. In conclusion,unknown compound X is a mixture of at least two compounds amongst which is the referencecompound a (the same Rf in the two solvents) and one other compound which is not b. Atypical application of this approach is the separation of amino acids.

5.2 Characteristics of TLC

TLC applies physico-chemical phenomena more complex than HPLC:

• TLC corresponds to a three-phase system between which equilibriums areestablished: solid (stationary), liquid (mobile) and vapour phases.

• The stationary phase is only partially equilibrated with the liquid phase beforethe migration of the compounds. Depending upon the manner in which theseparation is obtained, the mobile phase may or may not be in equilibriumwith the vapour phase.

• The adsorption phenomenon of the stationary phase is substantially reducedonce a large part of the adsorption sites are occupied. This creates an effect ofelongation of the spots. As a result, the Rf (retardation factor) of a compoundin the pure state is slightly different from the Rf of the same compound presentin a mixture.


Time (min)

A

B

Mig

ratio

n di

stan

ce0 2 4 6 8 10 12 14 16

Figure 5.4 Migration distances of the mobile phase on a TLC plate. Over a sequence of regulartime intervals, the quadratic progression of the eluant front can be seen. Curve A was obtainedin a chamber unsaturated with eluant vapour. Curve B was obtained by saturating the chamberwith eluant vapour.

• The flow rate of the mobile phase cannot be modified in order to improve theefficiency of a separation. A remedy to this problem is the multi-developmenttechnique, by drying the plate before each new cycle of migration.

• The speed of migration of the solvent front is not constant. It follows acomplex function in which the size of the particles of the stationary phase playa part. The migration velocity can be described by a quadratic law : x2 = ktwhere x represents the distance of the migration front, t the time and k is aconstant (Figure 5.4). As a result the resolution between two spots dependsgreatly on the Rf values of the compounds. Resolution attains a maximumfor an Rf value generally around 0.3.

To sum up, the efficiency N of a TLC plate is very variable. The height equivalentof a theoretical plate has, as in HPLC, an optimal value.


Many physico-chemical parameters and several factors must be taken into accountwhen choosing a good stationary phase. The size of the particles, their specificsurface area, the volume of the pores and the distribution of particle diametersare all factors that define the properties of the stationary phase. For nano-TLCthe size of the particles is of the order of 4�m and the pores are 6 nm.

The ratio between the silanols and siloxane groups determines the more or lesspronounced hydrophilic character of the phase. As with HPLC, it is possible touse bonded silica in which various chains are bound by covalent bonds to silanolgroups on the surface. Some phases incorporate alkyl chains (RP-2, RP-8, RP-18), while others contain organic functional groups (nitrile, amine, or alcohol),


MethyltestosteroneAlcohol, weakly polar

CortexoloneDiol, moderated polar

HydrocortisoneTriol, very polar

Reversed phase(acetone/water 60:40 v/v)

Si-60 NH2 CN RP-2 RP-8 RP-18 Si-60 NH2 CN RP-2 RP-8 RP-18

RfRf

0,80,8

0,60,6

0,40,4

0,20,2

00

Me

MeMeOH

O

Me

MeOH

O

O CH2OH

Me

MeOH

O

O CH2OH

HO

Normal phase(hexane/acetone 80:20 v/v)

Figure 5.5 Study of the separation of three steroids of different polarities upon six stationaryphases with two binary solvent systems. Evolution of the Rf values and inversed migration causedby the change of the eluting mobile phase, one polar and the other non-polar (reproducedcourtesy of Merck).

allowing these phases to be used with numerous mobile phases having the appro-priate pH and salt concentrations (Figure 5.5). TLC plates can also be preparedto contain chemical groups with net positive or negative charges on the surface.This type of plate is used for ion-exchange TLC.

Modified cellulose supports are also used in TLC, either as fibres or chemicallymodified micro-crystalline powders. The most widely known is DEAE-cellulose, aphase fairly basic containing diethylaminoethyl groups. Other polar phases, withion exchange properties can be employed for the separation of ampholytes.

� Mineral binders such as gypsum make the stationary phase fragile, yet serve toadvantage to recover the compounds after their separation. This can be done byscraping the zones of interest from the support and extracting the present compoundswith a solvent.

5.4 Separation and retention parameters

Each compound is defined by its retardation factor Rf (unitless) that correspondsto its relative migration compared to the solvent. Rf values lie between 0 and 1.

5.5 QUANTITATIVE TLC 123

Rf = Distance run by the solute

Distance run by the solvent front= x

x0

(5.1)

The efficiency N of the plate for a compound whose migration distance is x andspot diameter w is given by Equation 5.2 and H (HETP) through Equation 5.3:

N = 16x2

w2(5.2)

and

H = x

N(5.3)

In order to calculate the retention factor k of a compound or the selectivitycoefficient between two compounds, the distances migrated along the plate arecompared, for matching, with the migration times read on the chromatogram.Assuming that the ratio of the migration velocities u/u0 is the same on the plateas on the column (which is really only an approximation), then Rf and k can belinked:

Rf = x

x0

= u

u0

= t0

t= 1

k + 1

such that

k = 1

Rf

− 1 (5.4)

Rf values often depend on the solvent use in the TLC experiment and tempera-ture. Thus, the most effective way to identify a compound is to spot knownsubstances on the same plate, next to the unknown.

Finally, by comparison with expression 1.27, the resolution can be given by therelation:

R = 2x2 − x1

w1 + w2

(5.5)

5.5 Quantitative TLC

In order to use TLC as a quantitative method of analysis, it is essential to quan-tify the spots (Figures 5.1 and 5.6), along with definitions for all of the usualparameters (specificity, range of the domain of linearity, precision, etc.). This isdone by placing the plate under the lens of a densitometer (or scanner) that canmeasure either absorption or fluorescence at one or several wavelengths. Thisinstrument produces a pseudo-chromatogram that contains peaks whose areas canbe measured. In fact it is actually an isochronic image of the separation at thefinal instant. In TLC a spot is usually detectable if it corresponds at least to a fewng of a compound UV absorbent.


TLC plate

0 Rf 1

Migration distance (scale arbitrary)

Plate type RP-18UV detection at 254 nmEluting phase: acetone/water 50 : 50 v/vClimb: 20 min for 8 cm.

Me

MeR2

O

O CH2OH

R1

1 - Cortexone, R1 = H and R2 = H2 - Corticosterone, R1 = OH and R2 = H3 - Cortisone, R1 = O and R2 = OH

Rel

ativ

e ab

sorb

ance

(sc

ale

arbi

trar

y)

Orig

in

0 2 4 6 8

321

Solvent front

Figure 5.6 Separation of three steroids by TLC on a phase of reversed polarity. The migrationdistance increases with the polarity of the compound. This pseudo-chromatogram has beenobtained by scanning the TLC plate. The same separation effected by HPLC would lead toa chromatogram in which the order of the peaks would be reversed, a compound stronglyretained having the longest elution time.

� In order to reveal radioactively labelled compounds (�– emission), there existdensitometers that are equipped with a video camera giving an image of the radioac-tive distribution on the plate. The former procedure of autoradiography, obtained byputting a photoplate in contact with the TLC plate is rather insensitive (exposurescould take up to 48 hours). The new densitometers, known as Charpak machines,which are also used in gel electrophoresis, have sufficient sensitivity for detectingactivities in the order of a few Becquerels per mm2.

For many applications, TLC can replace HPLC (Figure 5.7). Although thistechnique requires more manual manipulations than HPLC, new improved toolsfor spoting, migrating, gradient elution, development and recording, confer thenecessary reproducibility. Compared with HPLC, TLC is able to treat more samplesin the same time period by the setting up of analyses in parallel on the same plate.The plate, only used once and disposable, allows for rapid sample preparationwith less risk of loss or contamination. It is very useful for biological samples.

The TLC plate on which the products have been separated is also a means,provisionally, to preserve very small samples after extraction, which can serve forother analyses (mass spectrometry for example).

A recent technological advance allows the eluent to migrate at a constant speedthrough the application of positive gas pressure in the migration chamber, aneffect especially developed which gains in both time and quality of separation.

PROBLEMS 125

Me

Me Me

O

O

Me

Me

O

OHH

MeMe OH

O

O CH2OH

HO

3

3

2

2

1

1

3. Hydrocortisone

2. Testosterone1. Progesterone

Mobile phase: Methanol : Water (70:30)CHROM7087

CHROM7065

TLC Prep-Screen C18 Econo-Prep HPLC

Figure 5.7 Comparison of TLC and HPLC. Separation of a mixture of three steroids on a TLCplate and on a HPLC column. This shows that it is possible to quickly perfect a separationby HPLC, using TLC at first, with the same stationary phase and the same mobile phase fordevelopment or elution (reproduced courtesy of Alltech).

High-performance thin layer chromatography HPTLC is an improvement of thetechnique where the sorbent material (e.g. silica gel 60) has a finer particle size anda narrower particle size distribution than conventional TLC. HPTLC plates havean improved surface homogeneity and are thinner. The resolution is improved,analysis times are shorter and it is sufficient to apply nanolitres or nanograms ofsample (Nano-TLC).

Problems

5.1 A mixture of two compounds A and B migrates from the origin to leavetwo spots with the following characteristics (migration distance x and spotdiameter w).

xA = 27 mm wA = 2�0mm

xB = 33mm wB = 2�5mm

The mobile phase front was 60 mm from the starting line.

1. Calculate the retardation factor Rf , the efficiency N and the HETP Hfor each compound.

2. Calculate the resolution factor between the two compounds A and B.


3. Establish the relation between the selectivity factor and the Rf of thetwo compounds. Calculate its numerical value.

5.2 The following figure represents the results of scanning a TLC plate in normalphase (mobile phase: hexane/acetone 80/20). The three compounds have thestructures A, B and C

Me

MeMeOH

O

Me

Me OH

O

O CH2OH

Me

Me OH

O

O CH2OH

HO

A

B

C

Rel

ativ

e ab

sorb

ance

(m

V)

Migration (arbitrary units)

Front

Start

20

40

0

60

80

100

1. Indicate compounds A, B and C, from the identification of the threeprincipal peaks of the recording.

2. What would have been the order of elution of these compounds ifexamined by an HPLC column containing the same types of stationaryand mobile phases?

3. What would have been the order of elution of these compounds ifexamined by an HPLC column containing a phase of type RP-18 witha binary mixture of acetonitrile/methanol (80/20) as eluent?

4. Calculate the Rf and the HETP for the compound which migratesfastest upon the plate (use the transposed formulae of column chro-matography, in particular that giving efficiency, with x as distance ofmigration).

6Supercritical fluidchromatography

Supercritical fluid chromatography (SFC) employs, as its name suggests, a fluidin the supercritical state as its mobile phase. This leads to improvements in theseparations of thermolabile compounds and more generally for compounds ofhigh molecular weight. The instrument is conceptually a hybrid of gas chromato-graph and liquid chromatograph, with either GC capillary columns or HPLCcolumns, the latter being preferred. The late arrival of this technique on theinstrumental market (about 1982), has been a handicap to its development,partly due to the fact that normalized methods have already been developedusing other classic chromatography techniques. In addition to this argument thefact that the apparatus is more complex and expensive has meant that unfortu-nately few instrument manufacturers have been interested in the realization ofcorresponding analytical instruments. This presentation will aim to highlight thebenefits of SFC.

6.1 Supercritical fluids: a reminder

The transformation of a pure compound from a liquid to a gaseous state and viceversa corresponds to a phase change that can be induced over a limited domainby pressure or temperature. For example, a pure substance in the gaseous statecannot be liquefied above a given temperature, called the critical temperatureTC, irrespective of the pressure applied to it. The minimum pressure required toliquefy a gas at its critical temperature is called the critical pressure PC (Figure 6.1).These points are the defining boundaries on a phase diagram for a pure substance.The curve, which limits the gas and liquid domains, stops at the critical pointC. Under these conditions, gas and liquid states have the same density. Abovethese temperatures and pressures, the compound becomes a supercritical fluid. Inparticular the viscosity of a supercritical fluid is almost that of a gas (Table 6.1).


128 CHAPTER 6 – SUPERCRITICAL FLUID CHROMATOGRAPHY

Solid

Liquid

Sub-critical domain 1(P > Pc and T < Tc)

Supercritical domain(P > Pc and T > Tc)

Sub-critical domain 2(P < Pc and T > Tc)

Critical domain(P = Pc and T = Tc)Critical point

Temperature °C

Triple point

“Dense gas”

Pre

ssur

e (M

Pa)

C

30

10

5

0T

Domainof principal use

Gas

−78 −60 −40 −20 0

(+31°/7.4 MPa)

(−57 °/ 0.52 MPa)

20 40 60 80

CO2

Figure 6.1 Phase diagram temperature/pressure of carbon dioxide. There exists for each puresubstance a relation between three variables: temperature T, pressure P and volume V, knownas the equation of state. The diagram above is the projection (P/T)for CO2. The critical pointis located at 31 �C and 7.4 MPa (1Mpa = 106 Pa, or 10 bar). Getting round the critical pointrenders it possible to go from the liquid state to the gaseous state without a discontinuity ofphase.

Table 6.1 Comparison of densities, viscosities and diffusivities for liquid, supercritical fluidand gas

State Density (g/mL) Viscosity �poise × 103� Diffusivity �cm2/s × 103�

Liquid 0.8–1 3–24 0.005–0.02Sup. fluid 0.2–0.9 0.2–1 0.01–0.3Gas 0.001 0.05–0.35 10–1000

Furthermore its solvation properties (governed by the distribution coefficient K)are similar to those of a slightly polar organic solvent. In this way carbon dioxide,under 300 bars and at 40 �C, is comparable to benzene for chromatographicapplications.

Depending upon the choice of temperature and pressure, the behaviour of asupercritical fluid can sometimes looks like a dense gas and sometimes like a liquid.For these reasons, use of supercritical fluids as mobile phases in chromatographypresents certain advantages.

� Carbon dioxide in its supercritical state can be used for the extraction, on a labo-ratory scale, of unstable compounds from the matrix. Many industrial applicationsuse also this methodology to extract food products (e.g. decaffeination, recoveryof aromas and spices, elimination of fats) or simply as a dry cleaning agent for

6.2 SUPERCRITICAL FLUIDS AS MOBILE PHASES 129

clothing. This non-flammable fluid has the advantage that it can be eliminated at lowtemperature without leaving any toxic residue. For these applications it is consid-ered as a green chemistry partner. However, the use of high pressures linked withlarge volumes introduce safety concerns and create potential hazards in industrialinstallations.

6.2 Supercritical fluids as mobile phases

Carbon dioxide is the standard in SFC because its supercritical state is relativelyeasy to reach (TC = 31 �C and PC = 7400kPa) (Figure 6.1). Beyond these values,the supercritical domain is attained. This low cost compound is not very toxic,non-flammable, non-corrosive. The main disadvantage is it inability to elute verypolar or ionic compounds.

More rarely used are nitrous oxide �N2O� TC = 36 �C�PC = 7100kPa� orammonia NH3� TC = 132 �C�PC = 11 500kPa�.

The density and therefore the solvating power of supercritical fluids variesaccording to the pressures to which they are submitted. As a consequence, apressure gradient in SFC is equivalent to an elution gradient in HPLC, or atemperature gradient in GC.

If the chromatograph can accommodate a double gradient of temperature-pressure, combined with an organic modifier (to displace the coordinates of thecritical point), it becomes possible to finely tune the retention of analytes andtherefore to modify their selectivities � (Figure 6.2).

P (MPa)

k

4

3

2

1

00

1015

2025

1

2

3

5 1030

40 50

20

0

0.5

P (MPa)

1

40 °C

70 °C

100 °C

150 °C

d (g

/mL)

Figure 6.2 Density for carbon dioxide as a function of pressure at four different temperatures. Atthe critical point, the density of CO2 is of 0�46g/cm3. Right, the figure represents the variation ofthe retention factor k for three alkaloids analysed under identical conditions and pressure, fixedby a restrictor at the outlet of the column (T = 40 �C, modifier 5% water and 15% methanol;1: codeine, 2: thebaine and 3: papaverine). The greater the increase in pressure the further theretention factor is reduced.


At 16 000 kPa and 60 �C carbon dioxide has a density of 0.7 g/mL (Figure 6.2).This is why the expression ‘dense gas’, is used in order to indicate that it is not aclassic gas. To compensate its low polarity, which under these conditions is similarto that of toluene, an organic modifier (or enhancing agent) such as methanol,formic acid or acetonitrile is frequently added.

6.3 Instrumentation in SFC

The instrumentation for SFC represents hybrid assemblies of GC and HPLCinstruments (Figures 6.3 and 6.4). To assure the flow rate of the supercrit-ical fluid a syringe pump or a reciprocal pump is used, which is maintainedbelow the critical temperature by means of a cryostat regulated at around 0 �C.In instances where an organic modifier is added, either a second pump or atandem pump is utilized which has two chambers, one for the supercritical fluidand the other for the modifier. The liquid then passes through a coil main-tained above the critical temperature in order to convert it to a supercriticalfluid.

A main difference between SFC and HPLC instrumentation is the need fora back-pressure regulator in SFC, whose function is to restrict outlet flow insuch a way to maintain the mobile phase in a supercritical state from the pumpthrough to the end of the column, or even as far as the outlet of the detectordepending upon the type chosen (Figure 6.3). The pressure regulator (also called

mixingchamber

Detector

Chromatogram

Heating

CO2

MeOH

Waste

Injectorvalve (pressure

regulator outlet)

0°C 40°C

Modifier

Restrictor

Coolingdevice Pump A

Pump B

Column

Figure 6.3 Schematic of a SFC installation using a HPLC packed column. Carbon dioxidereaches a supercritical state between the pump and the injector. A pressure regulator(‘restrictor’), is located after the column and either before or after the detector, dependingupon its type. It maintains the mobile phase under supercritical conditions until the outlet ofthe column; A modifier added in small quantity (less than 10 per cent) enables to control theselectivity of the analytes (diagram based upon a document from Vydac).

6.4 COMPARISON OF SFC WITH HPLC AND GC 131

1

2

3

4

1 - Oven for column2 - UV detector3 - Carousel type autosampler/injector4 - Refrigerated pump

Figure 6.4 A commercial SFC installation. The oven where the column is located also controlsthe mobile phase pre-heating. The pump is cooled to 0 �C (reproduced courtesy of Berger)

the restrictor) must correctly manage the important cooling procedure and theconsequent volume expansion when the supercritical phase returns to the gasstate at atmospheric pressure. Note that the presence of this restrictor avoidsthe large pressure drop across the column which is considered as a drawback ofHPLC.

With a FID (a flame ionization detector, which functions at atmospheric pressure)the restrictor is situated before the detector, while it is located after for detectorsbased upon UV-absorption, fluorescence or light diffusion.

A large variety of normal phase HPLC columns (packed type) or GC columns(capillaries) are used. These two types of columns are complementary. For apacked column of HPLC type, the high flow rate of the supercritical mobilephase will render detection by FID or coupling with a mass spectrometer moredifficult. Adding a modifier to the supercritical fluid would have the sameeffect.

6.4 Comparison of SFC with HPLC and GC

SFC is complementary to the other classic techniques of GC or normal phaseHPLC. The migration of the solute results from a distribution mechanism betweenthe apolar stationary phase and a slightly polar eluting mobile phase. The solvationcapacity of the mobile phase is governed by both temperature and pressure ofthe supercritical fluid. Therefore as the density of the supercritical fluid mobilephase is increased, components retained in the column can be made to elute. Theresistance to mass transfer between the stationary and the mobile phases is lessthan in HPLC because diffusion is about ten times greater than in liquids. The Cfactor in Van Deemter’s equation being smaller, the velocity of the mobile phasecan therefore be increased without an appreciable loss of efficiency (Figure 6.5).Moreover, as the viscosity of the mobile phase is close to that of a gas, GC


0 0.2 0.4 0.6 0.8 1 1.2

cm/s

5H

ET

P (

μm)

10

15

20

SFC

HPLC

Figure 6.5 Comparison between HPLC and SFC. Both experimental curves have been obtainedusing the same compound on the same column, but, in one, a classic liquid phase and in theother, carbon dioxide in a supercritical state. The HETP are comparable – but the separationcan be up to three times faster by SFC, thus saving analysis time.

capillary columns can be used. However, as a consequence of the position of therestrictor, the pressure drop across the column modifies the distribution coeffi-cients of the compounds between the beginning and the end of their migration.This causes peak broadening. For this reason SFC can provide separations atlow temperatures but the efficiencies met in capillary GC are not to be realizedwith SFC.

Polarity PolaritySpeed

Sensitivity Mol. weight

EfficiencyN

Selectivityα

Retentionk

Selectivedetection

Speed

Sensitivity Mol. weight

EfficiencyN

Selectivityα

Retentionk

Selectivedetection

weakly polar

HPLC SFCPacked column

Polarity versus supercritic fluid compositionvery polar

Figure 6.6 Comparison of SFC with HPLC packed columns. When mixed with methanol andadditives, supercritical carbon dioxide allows the rebuilding of the whole range of polaritiesrequired by the principal types of analyte.

6.5 SFC IN CHROMATOGRAPHIC TECHNIQUES 133

FID signal

Time (min)40 50 60 700 10 20 30

Mobile phase: CO2, supercriticalColumn DB5, 10 m × 50 μm, df = 0.2 μmDetector: FIDLinear temperature program

Figure 6.7 Spectacular SFC chromatogram of a mixture of polysiloxane oligomers (repro-duced courtesy of Fisons Instruments Inc.). Each compound leads to a unique peak on thechromatogram, thus allowing the determination of the distribution of molecular forms in apolymerization reaction.

6.5 SFC in chromatographic techniques

SFC is potentially useful for various applications (Figures 6.6 and 6.7). The abilityto vary selectivity by programming the parameters P (pressure) and T (tempera-ture) rather than by modifying the chemical composition of the eluent representsthe technique’s major difference. The low viscosity of the mobile phase permitsan arrangement of several HPLC-type columns in series. The range of compoundsanalysed by SFC includes lipids and oils, emulsifiers, oligomers and polymers(Figure 6.7), compounds of molecular mass greater than 1000 which cannot bestudied in GC. SFC offers superior speed and efficiency compared to HPLC.Finally, use of supercritical carbon dioxide as a mobile phase facilitates couplingwith a mass spectrometer or an infrared spectrophotometer and even with anNMR spectrometer.

7Size exclusion chromatography

Size exclusion chromatography (SEC) is a method by which molecules can be sepa-rated according to their size in solution, thus relating indirectly to their molecularmasses. To achieve this, stationary phases contain pores through which compoundsare able to diffuse to a certain extent. Although the efficiency of separation cannever attain that observed with HPLC, SEC has become an irreplaceable tool toseparate natural macromolecules in order to study the distribution of syntheticpolymer masses. Though the separation of compounds according to their sizesis not the most efficient process for small and medium molecules, this approachremains very useful in industry where the products are most often mixtures ofcompounds of very different masses. The instrumentation is comparable to thatused in HPLC.

7.1 Principle of SEC

Size exclusion chromatography (SEC) is based upon the ability of the samplemolecules to penetrate into the highly porous ‘bead’-like structure of the stationaryphase (Figure 7.1). Separation arises only as a result of the different degreesof penetration. Molecules of comparatively smaller weight are slowed in theirprogression in the column because they can enter into the stagnant mobile phasewithin the pores of the packing. This method is referred to as gel filtration chro-matography (GFC) when the stationary phase is hydrophilic (the mobile phasebeing aqueous) and as gel permeation chromatography (GPC) when the stationaryphase is hydrophobic (the mobile phase being a non-aqueous system).

The total volume VM of the mobile phase in the column can be considered asthe sum of two values VM = VI + VP: the interstitial volume VI (external to thepores) and the volume of the pores VP.

VI, called the void volume, represents the volume of mobile phase necessary totransport a large molecule assumed to be excluded from the pores and VM is thevolume accessible to a small molecule that can enter all the pores of the packing(volume VS).


136 CHAPTER 7 – SIZE EXCLUSION CHROMATOGRAPHY

Total exclusion volume

Total permeationvolume

log M

Elution volumeVR = VI + KSECVP

0

Selective permeationrange

2

3

4

5

1

1 2 3

2 3

0 vi vP VM

Gel particlesof the stationary phase

Figure 7.1 Migration across a stationary phase packing. Left, illustrative description of separa-tion in SEC by a porous packing according to the size of the pores. The non porous part ofthe bead, called the backbone, is inaccessible to the sample molecules. Right, a chromatogramdisplaying the separation of three species (1, 2, 3) of different sizes. The large molecules(excluded) 1 are the first to arrive followed by medium sised molecules (partial access) 2, andfinally by the smallest (full access) 3. The elution volumes VR are located between VI for KSEC =0and VM for KSEC = 1.

The general expression giving the retention (or elution) volumes VR are therefore(see Section 1.5)

VR = �VI + KSECVP� + KVS (7.1)

KSEC, the diffusion coefficient, represents the degree of penetration of a speciesdissolved in the volume VP�0 < KSEC < 1�. Ideal SFC retention is only governedby the continuous exchange of solute molecules between the void volume and thestagnant mobile phase within the pores. If these conditions are attained, Nernstcoefficient K is equal to zero and retention volumes VR are comprised between VI

and VM, giving:

VR = �VI + KSECVP� (7.2)

For the majority of modern packing materials, VI and VP are both of the order of40 per cent of the volume of the empty column.

When VR/VM is greater than 1, the behaviour of the compound on the columnno longer follows rigidly the mechanism of size exclusion but as in HPLC itundertakes physico-chemical interactions with the support (K > 0).

Each stationary phase is adapted to a separation range expressed in terms oftwo masses; a higher mass and a lower mass, above and below which there is noobtainable separation. Molecules whose diameter is larger than those of the greatestpores are excluded from the stationary phase �KSEC�. This explains the expression

7.2 STATIONARY AND MOBILE PHASES 137

size exclusion for this situation. They flow through the column without beingretained or separated. They appear as a single peak in the chromatogram atthe position VI (Figure 7.1). In contrast, the retention volume of the very smallmolecules is represented by VR =VM (in this case, KSEC = 1).The larger the part ofsample molecules in the pores, the larger the retardation. To increase this rangeof separation, which is fixed by the difference between these two volumes, twoor three columns can be put in a series, solvents of low viscosity are used andcolumn are occasionally warmed. The diffusion coefficients KSEC are independentof the temperature.

7.2 Stationary and mobile phases

SEC stationary phases are constituted of reticulated organic polymers or mineralsthat are used as porous rigid or semi-rigid beads (3 to 20�m). Pores diametersare within the 4–200 nm range. These packings, usually called gels, must withstandthe pressure at the head of the column and the temperature until about 100 �C inorder to allow their utilization for various applications.

A reduction in the diameter of the particles – a gauge for efficiency – reducesthe interstitial passages, rendering migration more difficult for the large, excludedmolecules. For this reason, it is preferable to increase the size of the particlesand to compensate by using a longer column. Standard columns have a length of30 cm, (with an internal diameter of 7.5 mm). Their efficiency N can attain 105

plates/m.SEC is sub-divided into two techniques:

• gel permeation chromatography (GPC). The material packing most often usedis a copolymer styrene-divinylbenzene (PS-DVB) with an organic mobile phasesuch as tetrahydrofuran, a good solvent for most polymers. Trichloromethaneas well as hot trichlorobenzene are also employed to dissolve synthetic poly-mers that are not soluble in other solvents (Figure 7.2). GPC is mainly usedin chemical analysis.

• gel filtration chromatography (GFC). For aqueous SEC, stationary phases mustbe hydrophilic. Some are based upon a PS-DVB base particle that is madebiocompatible with a hydrophilic coating containing hydroxyl or sulfonicgroups. Others are based upon polyvinyl alcohols either pure or copolymer-ized with polyglyceromethacrylates or vinyl polyacetates (Figure 7.3). Thesepackings are called gels since they swell on contact with aqueous mobilephases. Porous silica gels containing hydrophilic surfaces are equally employed(presence of glyceropropyl groups) �≡ Si�CH2�3–O–CH2CH�OH�CH2OH��).Adsorption phenomena �K > 0� are weak, even for the small molecules.GFC is mainly used to separate bio-polymers (e.g. polysaccharides) or otherwater-soluble biological macromolecules (e.g. proteins).


1 - C32 M = 4502 - C22 M = 3103 - C16 M = 2264 - C12 M = 170

Saturated linear hydrocarbons Phthalic diesters

mL 12

1 - Dioctyl phthalate MW = 390MW = 278MW = 222MW = 194MW = 92

2 - Dibutyl ,, 3 - Diethyl ,,4 - Dimethyl ,,5 - Toluene

1

2

3

4

1 2

8 106

3 4 5

10 mL 1612 14

Conditions: Column, PLgel 5 µm, Pores, 5 nm, Dimensions, 300 × 7.5 mm.Eluent: tetrahydrofurane. Flow-rate: 1 mL/min.

Figure 7.2 GPC. When the stationary phase has small pores, organic compounds of small tomedium molecular weight can be separated. In the chromatogram in the right, toluene servesto measure VM (reproduced courtesy of Polymer Laboratories).

� The term gel filtration should not be confused with the current procedure of filtrationwhich would create the reverse effect. The larger molecules have a greater difficultythan the smaller ones in crossing the filter.

7.3 Calibration curves

For a given solvent, each stationary phase is described by a calibration curve madewith isomolecular standards of known masses, M: polystyrenes in THF, poly-oxyethylenes, pullulanes or polyethyleneglycols, etc. (Figure 7.3 and Table 7.1).The curves representing log M as a function of the elution volume have a sigmoidalshape. However, by combining stationary phases of differing porosities, manu-facturers can provide mixed columns for which the calibration curve are linearover a broader range of masses. These curves are fairly indicative since size andmass are not mutually dependent parameters when passing from one polymer toanother.

Table 7.1 Permeation range (Da) of three gels for various standard compounds

Standard G2000: 12.5 nm pores G3000: 25 nm pores G4000: 45 nm pores

Globuar protein 5000–100 000 10 000–500 000 20 000–7 000 000Dextran 1000–30 000 2000–70 000 4000–500 000Polyethylene glycol 500–15 000 1000–35 000 2000–250 000

7.4 INSTRUMENTATION 139

102 103 104 105 106 107 108

(a)

Pores diameter : G2000 : 125 Å; G3000 : 250 Å

G 2000

G 3000

Elution (mL) Elution (mL)

G 2000

G 3000

20 30 40

(b)

M (

dalto

ns)

M (

dalto

ns)

SP of gel fitration

SP of gel permeation

SP of gel permeationSP of gel filtration

4 6 8 10

Mixed gel

* PLgel 5 µm, pores 104Å

*** PLgel MIXED-B

** PLgel 5 µm, pores 103Å

*

**

***

M (Da)

102 103

103

103Å

104Å

102

104

104

104

105

105

105

106

106 106

107

107

108M (Da)

Figure 7.3 Characteristics of stationary phases used for gel filtration and GPC columns.(a) Graphs indicating the mass ranges for two phases in gel filtration and for three phasesin gel permeation; (b) Calibration curves �log M = f�V �� for these different phases obtainedwith proteins for gel filtration and with polystyrene standards for the others (known molecularweights). A weak slope from the linear section reveals a better resolution between neighbouringmasses. This is the case when the pores are of regular dimension. The curves log M = f�K�,more rarely studied, reveal the same aspect (reproduced courtesy of Tosohaas and PolymerLab.). To avoid protein aggregate formation, denaturing compounds are sometimes introducedto the aqueous mobile phase.

7.4 Instrumentation

Instrumentation is similar to that employed in HPLC excepting the columns whichare bigger. To increase the resolution it is customary to use two or three columns,with different porosities, in series.


Column

Nitrogenor air

PhotodiodeLaser source

Atomiser

40/200°C

Heateddrift tube

Atomisation

Evaporation

Detection

Figure 7.4 Evaporative light scattering detector. At the outlet of the column the mobile phase isnebulized under a stream of nitrogen, by a specially atomizing device. When a compound elutesfrom the column, the droplets under evaporation give a suspension of fine particles. Illuminatedby a laser source they scatter the light from a lamp via the Tyndall effect (what happens iscomparable to the diffusion by fog through a car headlight beam). The signal detected by aphoto-diode is proportional to the concentration of the compound illuminated. Irrespectiveof the substance, the response factors are very close. This detector is only useful for samplecomponents that cannot be vaporized in the heated section of this detector.

The most commonly used detector is the refractive index detector (cf.Section3.11.3), considered asuniversal since forpolymers a variationof the refractiveindex is at first approximation independent of the molecular mass. As this detectoris not very sensitive, other detectors are sometimes added to it. They are based uponthe light absorption (UV detector) or fluorescence or light scattering (Figure 7.4).This last detector provides a more uniform response to structurally similar analytesthan do light absorbtion detectors. Users can create a universal calibration set from asingle analyte to quantify all analytes of the same class.

7.5 Applications of SEC

The main applications are found in the analysis of synthetic polymers or bio-polymers because this method permits the separation of nominal masses rangingfrom 200 to more than 107 Da. The absence of a chemical interaction with thestationary phase, associated with a rapid elution time and the possibility to recoverall of the analytes, convey many advantages.

7.5 APPLICATIONS OF SEC 141

Polystyrenestandards

(MW)

1 - 8 500 0002 - 1 030 0003 - 156 0004 - 28 5005 - 3 250

6 - 3 040 000 7 - 330 000 8 - 66 000 9 - 9 20010 - 580

log

M (

Da)

2 Columns, PLgel-MIXED-B 10 µm300 × 7,5 mm end to endEluent, tetrahydrofurane

Flow-rate, 1 mL/minInjection 25 µL (conc., 0.1%)UV Detection

1

189 12 15Min (or mL)

189 12 15Min (or mL)

7

56

432

23 4

5

6

78 9

10

Figure 7.5 Determination of molecular weight in a SEC experiment. The column can be cali-brated by using two complementary mixtures of polystyrene standards. Log molecular weightversus retention volume plot. This curve is linear over a wide range of masses due to the use ofa mixed stationary phase. Bottom right, conformation supposed for a lipophilic rod or randomcoil polymer in an aqueous solution. The resulting volume is called hydrodynamic volume ofthe macromolecule.

The choice of stationary phase best adapted to a given separation is made byconsultation of the calibration curve of various columns. The column of choiceis that which presents a linear range over the masses of the compounds formed inthe sample (Figure 7.5). The calibration must be carry out with the same type ofstandards, because macromolecules can have a variety of forms, from pellet liketo thread like (Table 7.1).

7.5.1 Molecular weight distribution analysis

Synthetic polymers differ from small molecules in that they cannot be characterizedby a single molecular weight. Even in its pure state, a polymer corresponds toa distribution of macromolecules of different weights. SEC chromatograms andintegrated peak areas allows the determination of the molecular weight distribution


Separation of the constituents in corn-syrup

Column, HPX-42AEluent, waterTemp. 85°CDetection, refractive index

1: Glucose M = 1802 to 11: (Glucose-18)nwithin somewherebetween 2 and 11M = 180 × n-18(n-1)

4 8 12mL 105 15 20 mL

Separation of a mixture of peptides

Column, Superdex (Dextran)Eluent, waterUV detection (214 nm)

1 - Cytochrome C2 - Aprotinine3 - Gastrine I4 - Substance P5 - (Gly)66 - (Gly)37 - Glycine

M = 12500

vivM

1

23

45

67

8

11–9

1

23

5

67

4

650021261348

36018975

Figure 7.6 Gel filtration chromatogram. Left, separation of a mixture of glucose oligomersranging from a single unit (glucose M =180), up to 20 units (M around 3000) (reproduced cour-tesy of Polymer Lab). Right, separation of a mixture of diverse proteins and glycine oligomers(reproduced courtesy of Pharmacia-Biotech).

as well as the most probable mass and the mean mass. This assumes that the massand the molecular volumes are directly related. Furthermore, the calibration ofthe column must be done with standards of the same family and with the samemobile phase flow rate.

7.5.2 Other analyses

SEC, which allows high-speed separations, is used for control analysis of sampleswith unknown compositions. These samples usually contain polymers and smallmolecules, which is often the case for numerous commercial or industrial products,such as in the biodegradation of polymers.

For typical organic compounds, which can readily be analysed by HPLC or GC,there are fewer applications unless they are sugars or polysaccharides (Figure 7.6)such as starch, paper pulp, beverages and certain pharmaceuticals. SEC with gelcolumns are widely used for aqueous separations of bio-molecules.

PROBLEMS 143

Problems

7.1 Occasionally in SEC values of K > 1 are observed. How might thisphenomenon be accounted for?

7.2 Gel permeation chromatography is to be used to separate a mixture offour polystyrene standards of molecular mass: 9 200, 76 000, 1�1 × 106 and3 × 106 daltons. Three columns are available for this exercise. They areprepacked with gel with the following fractionation ranges for molecularweights:

A � 70000 to 4 × 105 daltons

B � 105 to 1�2 × 106 daltons

C � 106 to 4 × 106 daltons

How might these four polymers be separated in a single operation if it ispermitted to use two of the above columns end to end?

7.3 A solution in THF of a set of polystyrene standards of known molecular masswas injected onto a column whose stationary phase is effective for the range400–3 000 daltons. The flow rate of the mobile phase (THF) is 1 mL/min.The chromatogram below was obtained.

4 5 6 7 8 9 min

34 500

92003250 580 162

1. Plot the log of relative molecular mass vs. retention volume.


2. What is the total exclusion volume for the column (i.e. the interstitialvolume), and what is the volume of the pores (the intraparticle volume)?

3. Calculate the diffusion coefficient KSEC for the polystyrene standardwhose relative molecular mass is 3 250 daltons.

8Capillary electrophoresis andelectrochromatography

Capillary electrophoresis (CE) is a very sensitive separation method which has beendeveloped largely through the experience acquired from high performance liquidchromatography, thin layer chromatography and from electrophoretic methods.Bio-molecules and compounds of lower molecular mass, difficult to study byHPLC or classical methods of electromigration on slab gel, become separable byCE. From now on, high performance capillary electrophoresis (HPCE), suitedto automation, has replaced the traditional electrophoretic techniques on gels.CE, officially recognized by several regulatory agencies, the FDA among them,included in the pharmacopoeia, can be used for quantitative analysis. Capillaryelectrochromatography (CEC) is a relatively new hybrid separation method thatcouples the high separation efficiency of CE with HPLC.

8.1 From zone electrophoresis to capillaryelectrophoresis

Capillary electrophoresis corresponds to an adaptation of the more general elec-trophoresis methodology. This separative technique is based upon the differentialmigration of the species, whether or not they carry an overall electric charge,present in the sample solution, under the effect of an electric field and whensupported by an appropriate medium.

In the classic semi-manual electrophoretic technique used mainly in bio-analysis, a small slab or strip of plastic material covered by a porous substance(a gel) is impregnated with an electrolyte buffer. The two extremities of the coveredgel system are dipped into two independent reservoirs containing the same elec-trolyte and linked to the electrodes of a continuous voltage supply (Figure 8.1).The sample is deposited in the form of a transverse band, which is cooled and thenbedded between two isolating plates. Under the effect of several parameters that


146 CHAPTER 8 – CAPILLARY ELECTROPHORESIS AND ELECTROCHROMATOGRAPHY

pd 300 – 600V

Cover

Strip

Electrolyte buffer reservoirs

Diaphragm

CatholyteAnolyte

–+

a typical developed film

O

O

OH

O

O

OH

OH H

OH

O

O

O

ninhydrin

N

+ ninhydrine

+

“Ruhemann purple”

λabs : 570 nm

-NH3

-NH3

C

R

H CO2H

NH2

Products

Figure 8.1 Schematic of a horizontal electrophoresis apparatus. Top, each compartment isseparated by a diaphragm in order to avoid contamination of the electrolyte by secondaryproducts which are formed during contact with the electrodes. This technique is operated eitherat constant current or at constant voltage or at constant power. The flat gel is between twoplates of glass. Middle, aspect of a standard strip support after revelation. Bottom, ninhydrinis often used to reveal proteins or amino acids. This reagent is transformed on contact withan amino acid that it degrades, to an unstable compound intermediate which reacts in turnwith a second molecule of ninhydrin yielding ‘Ruhemann purple’ This reagent is one of severalcompounds existing (e.g. Fluorescamine) to determine position of particular species followingmigration on the strip. Horizontal gels offer many advantages for nucleic acid separation andremain a widely-used tool for the molecular biologist.

act jointly – voltage (500 V or more in the case of small molecules), charge, size,shape, temperature and viscosity – the hydrated species migrate from one end tothe other, generally towards the electrode or pole opposite sign on a time scale thatcan vary from a few minutes to over an hour. Each compound is differentiatedby its mobility but the absence of a measurable solvent front, compared to TLC,requires that the distance of migration is estimated in relation to that of a substance

8.1 FROM ZONE ELECTROPHORESIS TO CAPILLARY ELECTROPHORESIS 147

used as an internal marker. The detection of species, following migration, througha contact process, are transferred onto a membrane where they are derivatizedwith specific reagents as silver salts, or Coomassie Blue® (Figure 8.1). Markerscontaining radioactive isotopes (32P or 3H) can also be used to give traces that canbe exploited in the same manner as in TLC.

In capillary electrophoresis, the covered gel slab of the classic technique isreplaced by a narrow-bore open-ended fused silica capillary (15–100�m diameter).The capillary of length L, varying between 20 and 80 cm, is filled with an electrolyteaqueous buffer solution as the two reservoirs (Figure 8.2). For a better control ofthe migration time, it is advisable to place the capillary in a thermostatic oven.A small inner diameter of the capillary reduces Joule heating to negligible levelsand allows the use of high electric fields for very rapid separations (the voltageapplied to the electrodes can attain 30 kV).

+ –

Safety enclosure

Anode

Capillary

Electrolyte

HV Source

0 – 30 kV

Direction of migration

Cathode

Electrolyte

Detectionmodule

Effective lengthTotal length L –+

A typical electropherogram

2 64 510 3

2

64

1

5335

mA

U

Migration time (min)

mV

S

Separation of cations:

Capillary: 75 μm × 60 cm Electrolyte: “Ionselect”Conc. 1ppm each ionUV Detection: 214 nm

1 - NH42 - K3 - Ca

4 - Na5 - Mg6 - Li

Power Supply

Voltage: 20 kV (5 μA)

Figure 8.2 Schematic of a capillary electrophoresis instrument. The electrolyte is an aqueousionic solution, filtered, degassed and containing a variety of additives. A small volume of thesample is injected at the positive end of the capillary (cf. 8.3). For a voltage greater than5–600 V/cm (30 kV if L = 50 cm) special insulation becomes necessary to avoid shorts and arcsof current in a humid atmosphere. For safety reasons, one electrode is usually at ground. Theeffective distance of migration l is around 10 cm shorter than the length L of the capillary.Below is a typical electropherogram corresponding to the separation of several cations (ordinategiven in units of milli-absorbance). The electrolyte is a commercially available mixture. Thedistorsion of the peaks is due to electrodispersion. This phenomenon is caused by the differencesin conductivity, and hence field, in each zone. The peaks would be symmetrical if their speedswere closer together (reproduced courtesy of Waters).


A detector is placed near the cathode compartment, at a distance l from the headof the capillary. The signal obtained provides the baseline for the electropherogram(Figure 8.2) which yields information about the composition of the sample. Theonly species detected are those which are directed towards the cathode.

8.2 Electrophoretic mobility and electro-osmotic flow

Particles suspended in a liquid, like solvated molecules, can carry electric charges.The sign and size of the charge depend upon the nature of the species, that of theelectrolytic medium as well as on the pH (Figure 8.3). This net charge originatesfrom the fixation to the particle surface, of ions contained in the buffer electrolyte.

Under the effects of various phenomena or simultaneous actions such as temper-ature, viscosity, voltage, these particles will have migration velocities that will befaster, the smaller they are and the greater their charge. The separation dependsupon the charge-to-size ratio of the hydrated analyte ions.

For each ion the limiting migration velocity vEP results from the equilibriumbetween the electric force F , which is exerted in the electric field E acting on theparticle of charge q, and the forces resulting from the solution viscosity �. Neutral

CathodeAnode

––

++

1

Hückel equationif immobile electrolyte

+ –

Det

ecto

r re

spon

se

Migration time

Cations Neutral Anions

EOF

vappvEOS

vEP

frictional force(for a spherical ion)

electrical force

resulting vector

++ ––

vEP = qE6πηr

Figure 8.3 Hückel equation and typical electropherogram. Influence of the net charge, electricfield, volume of the ion and viscosity of the solution upon the migration velocity in an electrolyteanimated by an electro-osmotic flow (cf. Section 8.2.2). Higher charge and smaller size confergreater mobility, whereas lower charge and larger size confer lower mobility. The separationdepends approximately upon the charge-to-size ratio of each species. Uncharged species moveat the same velocity as the electroosmotic flow (see later). The smaller anions arrive last sincethey would normally go towards the anode. At low pH, electro-osmotic flow is weak and anionsmay never reach the detector.

8.2 ELECTROPHORETIC MOBILITY AND ELECTRO-OSMOTIC FLOW 149

species are poorly separated except if an ionic agent is added to the electrolyte inorder to associate with them.

Hückel proposed an equation taking account of the influence of these factorsupon the electrophoretic velocity vEP of an ion considered as a sphere of radius r .

The charged species present in the sample are submitted to two principal effects,which are their individual electrophoretic mobility and the more global electro-osmotic flow.

8.2.1 Electrophoretic mobility – electromigration

A compound bearing an electric charge move within the electrolyte assumed tobe immobile at a velocity vEP (m/s) which depends upon the conditions of theexperiment and of its own electrophoretic mobility �EP. For a given ion andmedium, �EP is a constant which is characteristic of that ion. This parameteris defined from the electrophoretic migration velocity of the compound and theexerted electric field E, using expression 8.1:

�EP = vEP

E= vEP

L

V(8.1)

In the above equation, L designates the total length of the capillary (m) and V thevoltage applied across the extremities of the capillary. A positive or negative sign isassigned to the electrophoretic mobility, according to the cationic or anionic natureof the species; �EP�m

2/V/s� is equal to zero for a globally neutral species. �EP canbe obtained from an electropherogram by calculating vEP of the compound in aknown electric field E (V/m), taking into account of the velocity of the electrolyte(cf. Section 8.2.2). This parameter depends not only on the charge carried by thespecies, but also on its diameter and on the viscosity of the electrolyte.

8.2.2 Electro-osmotic mobility – electro-osmotic flow (EOF)

The second factor that controls the migration of the solute is the electro-osmoticflow. This flow corresponds to the bulk migration of the electrolyte through thecapillary. In gel electrophoresis, this flow is small, but in capillary electrophoresisit becomes more important because of the internal wall of the capillary. It ischaracterized by the electro-osmotic mobility �EOS, as defined by a relation similarto 8.1. vEOS represents the velocity of the electro-osmotic flow.

�EOS = vEOS

E= vEOS

L

V(8.2)

In order to calculate �EOS, the electro-osmotic flow velocity vEOS must first bedetermined. This corresponds to the velocity in the electrolyte of a species without


any global charge. This is done by measuring the migration time tnm for a neutralmarker to migrate over the distance l of the capillary �vEOS = l/tnm�.

As a neutral marker, an organic molecule that is non-polar at the pH of theelectrolyte used and easily detected by absorption in the near UV, is selected (e.g.acetone, mesityl oxide or benzyl alcohol).

The electro-osmotic flow has several origins in relation with the internal wallof the capillary. A capillary made of fused silica not having been subjected to anyparticular treatment bears on its inner surface numerous silanol groups (Si-OH)which become ionized to silanoates (Si-O-) when the pH of the electrolyte risesabove 3. Under these conditions, a fixed polyanionic layer is formed that attractscations present in the electrolyte. These cations arrange themselves into two layersof which one is attached to the internal wall while the other remains slightlymobile (Figure 8.4). Between these two layers a potential difference (Zeta potential)develops, the value of which depends upon the concentration of the electrolyte andthe pH. When the electric field is applied, H3O

+ and ions being solvated by watermolecules migrate towards the cathode. In capillary electrophoresis instruments,the net effect of the electro-osmotic flow is to impose for all charged speciespresent in the sample the direction oriented from the anode towards the cathode.The anions progress in an anti-electro-osmotic fashion.

vEOF

E –

Water molecule

+

+

+

SiO

O–

O

O

pH

m2/V.s × 104

24

8

6

10

4 6 8 10

Doublelayer

+ ++

+++

+ +

+

+

+

+

+

+

vEOF × 104

Silicate glass wall

anode cathode

electro-osmotic flow

Rigid layer

Diffuse layer

– –

– ––

– – – –

+

Figure 8.4 Origin of the electro-osmotic flow in a capillary filled with an electrolyte. Model ofthe double layer. If the inner wall has not been treated (polyanionic layer of a silica or glasscapillary) then a pumping effect arises from the anodic to the cathodic compartment: this isthe electro-osmotic flow which is reliant upon the potential which exists on the inner surfaceof the wall. If the wall is coated with a non polar film (e.g. octadecyl) then this flow no longerexists. The electro-osmotic flow is proportional to the thickness of the double cationic layerattached to the wall. It is reduced if the concentration of the buffer electrolyte increases. vEOS ispH dependant: between pH 7 and 8 vEOS can increase by as much as 35 per cent.

8.2 ELECTROPHORETIC MOBILITY AND ELECTRO-OSMOTIC FLOW 151

+ + ++++

+ + ++++

++ + +

+

+

Silica wall

AnodeCathode

vEOF

E

– – – – – –

– – –

––

–

– – –

– +

Water molecule

+

Figure 8.5 Effect of a cationic surfactant upon the silica inner wall. As the migrations mustalways be made in the direction where the detector is, the voltage polarity of the instrument musttherefore be reversed in order for anionic species to progress naturally in the same direction asthe electrolyte, that is, toward the detector.

� Usually, a capillary with a negative inner surface generates a linear displacementof the electrolyte (an electro-osmotic flow) directed towards the cathode. In contrast,if a surfactant is added, such as tetra-alkyl ammonium, capable of reversing thepolarity of the inner wall, then the electro-osmotic flow is directed towards the anode(Figure 8.5). By treating the wall with an alkylsilane to make it hydrophobic, proteinsbecome separable, otherwise they tend to adsorb at the surface of bare fused silica.

8.2.3 Apparent mobility

According to the previous arguments, each ion has an apparent migration velocityvapp which depends on both the electrophoretic velocity and the electro-osmoticflow (relation 8.3):

vapp = vEP + vEOS (8.3)

vapp is easily calculated from the electropherogram. Using l the effective length ofthe capillary, and tm, the migration time, vapp is given by the expression:

vapp = l/tm (8.4)

The apparent electrophoretic mobility �app is defined by an expression analogousto 8.1 or 8.2, such that:

�app = vapp

E= vapp

L

V(8.5)

and, by consequence

�app = l · Ltm · V (8.6)


minutes

anions :1 Bromide

123

7

9

8

4

611 14

17

18

19

2022

23

2425

2628

27

29

3031

32

33 34 3536

37

2116

15

13

12

10

39.4

350

.58

3.0

4.0

5.0

6.0

9.0

10.0

11.0

8.0

7.0

5

2 Chloride3 Ferrocyanide4 Nitrite0 Nitrate6 Sulfate7 Azide8 Oxalate9 Molybdate10 Tungstate12 Fluoride13 Tartarate16 Phosphate17 Citraconate19 Carbonate20 Acetate24 Propionate26 Crotonate28 Butyrate31 Valerate33 Caproate37 Gluconate

Figure 8.6 An electropherogram. Separation of a complex mixture of anions. The lack of peaksymmetry (see also Figure 8.2), is due to variations in the electric field along the whole lengthof the capillary caused by the dynamic ionic composition (image courtesy of ATI Unicam).

By combining the electro-osmotic flow and the apparent mobility it is possible tocalculate the true electrophoretic mobility of the species carrying charges. Fromrelation 8.3 it can be written:

�EP = �app − �EOS

or alternatively

�EP = L · lV

· � 1

tm

− 1

tmn

� (8.7)

� HPCE is commonly used for the separation of anionic species. Generally thepolarity of the instrument is reversed in order to change the location of the detectorfrom the cathode end to the anode end of the capillary. As a result the electro-osmoticflow direction is also reversed. Only anions whose �EP values are greater than thoseof �EOS will be detected (Figure 8.6).

8.3 Instrumentation

8.3.1 Different modes of injection

To introduce a micro-volume of sample, which must not exceed 1 per cent of theeffective length of the capillary in order to protect the resolution, two proceduresare used:


• Hydrostatic injection. This action is achieved by dipping the end of the capillaryinto the solution (also an electrolyte) containing the sample while creatinga slight vacuum at the opposite end. The procedure can be improved byexerting a pressure of around 50 mbars upon the sample solution.

• Electro-migration injection. This technique, used in gel electrophoresis, isachieved by putting the sample at a potential of appropriate polarity comparedto the other extremity and briefly dipping the capillary into it. In contrastto the previous procedure this mode of injection induces a discriminatoryaction upon the compounds present, which leads to a non-representativecomposition of the sample.

The hydrostatic injection method is less precise than in HPLC because injectionloops do not exist for volumes between 5–50 nL. The quantity entering the capil-lary is dependent upon many of the parameters that appear in the well-knownPoiseuille expression which gives the flow rate F in a tube (radius r , length L)for a liquid having a dynamic viscosity � (expression 8.8). The application of thisformula results in an approximate value for what might be termed the ‘enteringflow rate’ in the capillary.

F = �P�r4

8�L(8.8)

This relationship reveals that if the radius of a capillary is doubled, then thevolume entering will be 16 times greater. This volume is also proportional to thedifference in pressure �P. An increase in the length of the capillary L produces

+

Detector

Source(a) (b)

Detector

Sugar (−CHO group)

Sugar−CH = N

HOHO

NH2

SO3HSO3H

SO3HSO3H

Figure 8.7 UV detection and post-separation derivatization. Analytes passing the light sourceabsorb UV radiation resulting in a decrease in light reaching the detector. (a) The measuringcell comprising the capillary itself. (b) Post-derivatization can be undertaken by cutting thecapillary just prior to the detector and by introducing an appropriate reagent. Below, exampleof a reaction to transform a sugar into a fluorescing derivative.


the reverse effect. An internal standard should be used to improve the quantitativeperformances of HPCE.

8.3.2 Detection methods

Many of the methods of detecting analytes in CE are similar to those used forliquid chromatography. Only three important methods are given here.

• Direct UV/Vis detection (cf. Chapter 9). Detection is usually done by UV-visible absorbance with a diode array detector. A very small window is createdby burning the polyimide protecting the capillary in such a way that UV lightcrossing the capillary can be measured. This design is very efficient as thedetector cell is basically part of the capillary, which avoids a dead volume(Figure 8.7). UV is most sensitive when used at low wavelengths.

• Fluorescence detection. This detection implies a derivatization of the analytes,which are chemically labelled with a flurophore. Then separation is performedas normal. A light source is used as a source of radiation, and as the analytesmove past the detection window the flurophores emit radiation at a differentwavelength. The sensitivity of this procedure is enhanced if a very intenselaser source is employed (Figure 8.7).

• Mass spectrometry detection. A mass spectrometer linked to a CE instrumentallows information on solutes molecular masses and provides structural infor-mation helping with the identification of unknowns. However, interfacing ofthe two instruments is not easy (cf. Chapter 16). Thus an extra flow of liquidmust be added to the CE eluent to obtain gas phase ions of the solutes. MSdetection is used especially in biochemistry analysis.

Abs

.A

bs.

Normal detection

Reverse detection

Capillary

Capillary

−0.01

−0.005

0.00

0.005

0.01

0.015Absorbance

oxal

ate

tart

rate

mal

ate

succ

inat

ela

ctat

eac

etat

epr

opio

nate

buty

rate

1 2 3 4 5 min

Figure 8.8 Separation of the principal organic acids in white wine by indirect UV detection. Malicacid and lactic acid are indicators for the malo-lactic fermentation (image courtesy of TSP)

8.4 ELECTROPHORETIC TECHNIQUES 155

� Indirect UV detection. This is used for analytes – as inorganic ions – which do notabsorb UV radiation. It involves using a buffer in the capillary such as a chromateor a phthalate which have high absorption coefficients under these experimentalconditions. As analytes move past the detector the amount of light passing throughthe capillary increases as UV absorbing buffer is excluded, leading to negative peaks(Figure 8.8).

8.4 Electrophoretic techniques

8.4.1 Capillary zone electrophoresis (CZE)

This mode of electrophoresis, in which the electrolyte migrates through the capil-lary, is the most widely used. In this mode, samples are applied as a narrow bandthat is surrounded by the electrolyte buffer. This electrolyte can be, dependingupon the application, acidic (phosphate or citrate) or basic (borate) or an ampho-teric substance (a molecule possessing both an acidic and an alkaline function). Theelectro-osmotic flow increases with the pH of the liquid phase or can be renderedinexistent. This procedure is also called, in contrast to CGE (cf. Section 8.4.3), freesolution electrophoresis.

8.4.2 Micellar electrokinetic capillary chromatography (MEKC)

In this variant of CZE, adapted to the separation of neutral or polar molecules,a cationic or anionic surfactant, e.g. sodium dodecylsulfate, is added in excessto the background electrolyte to form charged micelles. These small sphericalspecies, immiscible in the solution, form a pseudo-stationary phase analogous tothe stationary phase in HPLC. They trap neutral compounds efficiently throughhydrophilic/hydrophobic affinity interactions (Figure 8.9). Neutral molecules aswell as ionic species can then be conveniently separated as a direct result of theirsolubilization within the micelles.

MEKC is useful to perform chiral analyses. This involves the addition of acyclodextrin as a chiral selector to the running buffer. Optical purity analysis can bedetermined due to the formation of inclusion complexes between a hydrophobicportion of the solute and the cavity of the cyclodextrin, having different stabilities(cf. Section 3.7 and Figure 8.9).

8.4.3 Capillary gel electrophoresis (CGE)

This technique represents the transposition of the classic agarose or polyacrylamide(PAGE) gel electrophoresis into a capillary. The capillary is filled with an electrolyteimpregnated into a gel. This produces a filtration effect, which decreases the


cathode

R = 23

5 10Migration time (min)

Abs

orba

nce

(AU

× 1

0E-4

)

H

H H

CC

NH2

Me

Electroosmotic Flow

Figure 8.9 Separation of neutral compounds using surfactants (MEKC technique). Above, thelipophilic part of a surfactant, such as an alkylsulfonate, can bind moderately to certain moleculesof the substrate S. The negatively charged micelles are directed towards the cathode by theelectro-osmotic flow (adapted from Agilent technologies). Below, electropherogram of a racemicsample of an amphetamine in the presence of a cyclodextrin. The electrolyte, NaH2PO4 25 mmol(pH 2.5), contains 5 per cent of gamma-cyclodextrin polysulfate. At this pH the electro-osmoticflow is negligible. The hydrogenosulphate ions of the cyclodextrins being directed towardsthe anode collect the amphetamine molecules retained in their hydrophobic cavities. The twoenantiomers, in equal quantity, form two diastereomer complexes which migrate at differentvelocities. For this experiment the anode is on the detector side. (Reproduced courtesy ofBeckman Coulter Inc. USA).

electro-osmotic flow and minimizes convection and diffusion phenomena. Fragileoligonucleotides can be separated in this way.

CGE has been adapted to DNA sequencers. Special instruments fully automated(from sample loading to data analysis) have been designed with multiple capil-laries that can simultaneously analyze many samples through a fluorescent-baseddetection.

The modified technique is known as capillary array electrophoresis for theseparation of the DNA or RNA fragments based on their size.

� In classic zone electrophoresis, the support on which the migration takes place,can contain a polyacrylamide gel impregnated with the electrolyte. If the latter

8.5 PERFORMANCE OF CE 157

contains sodium dodecylsulfate, then the electrophoresis is named SDS–PAGE, afterits acronym. Separations are improved by a filtering phenomenon that superimposesto the electric forces.

8.4.4 Capillary isoelectric focusing (CIEF)

This technique consists of creating a stable and linear pH gradient in a surface-treated capillary, which has been filled with a solution that contains ampholytes.

Ampholyte or zwitterions. An ampholyte is a molecule that contains both acidicand basic groups. At a particular pH, known as the isoelectric point, the chargeon the groups is balanced and the molecule is neutral. If an ampholyte is placedin a pH gradient and electrophoresed it will migrate to the point at which it isuncharged and then stops moving.

At the anode side, the capillary is plunged into H3PO4 solution while on thecathode side, it is dipped into a NaOH solution. When an electric field is appliedto the extremities of a capillary filled with a mixture of solutes and ampholytes, apH gradient appears. Each of the charged analytes (generally, proteins) migratesthrough the medium until it reaches the region where the pH has the same valueas its isoelectric point (at its pI , the component net charge is zero). Then, bymaintaining the electric field and using a hydrostatic pressure, these separatedspecies migrate towards the detector. In order to ensure the high performance ofanalysis, standards of pI (pI markers) are needed. The high resolutions obtainedwith this procedure allow especially the separation of peptides whose pIs maydiffer by only 0.02 pH units.

8.5 Performance of CE

The performance of CE, for the separation of biopolymers is comparable to thatof HPLC. The success of a separation relies on the choice of an appropriate buffermedium adapted to the analysis. Only a very small quantity of sample is requiredand the reagent consumption or solvent is negligible (Figure 8.10). The sensitivityis very high: by using laser induced fluorescence (LIF) detection a few thousandsof molecules can be observed.

However, the reproducibility of the analyses is less certain than in HPLCbecause there are many subtle factors that can affect the precision of the injectedvolume. For hydrostatic introduction, relative standard deviation is of the orderof 2 per cent, if an internal standard is used. When the efficiency N of the sepa-rations is sufficiently large, it becomes possible to separate isotopes of an element(Figure 8.11).

HPCE in its ‘lab-on-a-chip’ version is at the frontier of classic chemistry andis particularly interesting to molecular biologists for the analysis of degradationproducts of proteins.


“DIET COLA”Caffeine, Aspartame and Benzoic acidElectrophoretic mobilitiefs

Time 0

Time t

Anode (+) Cathode (–)

Electroosmotic Flow

a– + b–

+ c

a– and b–

cb– a–

Time (min)

200210

220230

240250

260270

280290

300

0.0150

0.0118

0.0086

0.0054

0.0022

– 0.00101.00 1.50 2.00 2.50 3.00 3.50

Figure 8.10 Electro-kinetic separation of three species a− b− and c. Left, The electro-osmoticflow carrying all of the charged or neutral species along with it, is directed towards the cathode.The negative species though attracted by the positive pole cannot overcome the electro-osmoticflow and are therefore displaced towards the cathode. Right, separation of caffeine c and of theanions of aspartame a− and of benzoate b− from a sample of ‘DIET COLA.’ Presentation inthe form of a 3D electropherogram (reproduced courtesy of TSP).

0

0.0005

0.0010

0.0015

0.0020

35 40 45 50 min

Abs

orba

nce

35Cl–

37Cl–

Figure 8.11 Separation of chlorine isotopes. When the efficiency is very high isotopes of thesame element can be separated which as in this example leads to two clearly defined peaks.Conditions: capillary of 75�m/47 cmV =20kVT =25 �C, electrolyte: chromate/borate pH 9.2.McDonald LT. Anal Chem. 1995, 67, 1074.

The separation parameters (efficiency, retention factor, selectivity, resolution)are accessible from electropherograms by using either the same formulae as inchromatography, or those specific to HPCE.

The theoretical efficiency of a separation N – as high as one million plates/metrein a column of length L – can be calculated from its effective length l and from thediffusion coefficient D �cm2/s�. This latest parameter is linked to the dispersion� and to the migration time tm via Einstein’s law ��2 = 2D · tm�. Expression 8.9

8.6 CAPILLARY ELECTROCHROMATOGRAPHY 159

Flow Flow

Capillary electrophoresisor electrochromatography

Liquid chromatography

Open tube, inner diameter: 50–150 μm Packed column, inner diameter: 2–4 mm

Figure 8.12 Comparison of the conjugated effects of diffusion and of the mode of progression ofthe mobile phase in HPCE and in HPLC. Diffusion which increases as the square of the diameterof the tube is smaller in electrophoresis than in liquid chromatography, especially if the samplemixture comprises compounds of greater molecular mass. Elsewhere in CE, the electrolyte isdrawn along by the internal wall, while it is pushed in HPCE and in CE. Finally the profile ofthe hydrodynamic flow is almost perfectly flat and not parabolic as in HPLC.

is attained (or 8.10 if tm is eliminated by using expression 8.6). These expressionsmay be use also to calculate D if N is experimentally available.

N = l2

2Dtm

(8.9)

N = �app

2D· V · l

L(8.10)

Relation 8.10 reveals that the efficiency grows up with the voltage applied. Themacromolecules, for which the diffusion factors are slighter than those of smallmolecules, inevitably lead to better separations (Figure 8.12).

Finally in HPCE, the resolution R between two peaks can be calculated by usingthe efficiency N , the difference in the speed of migration of the two solutes ��v�and their average speed v (8.9):

R =√

N

4· �v

v(8.11)

8.6 Capillary electrochromatography

Capillary electrochromatography (CEC) is a separation method that borrows fromCZE and HPLC, by associating the electromigration of ions with their partitioningbetween the phases, typical to chromatography. Instead of a hydraulic pump,it is the high voltage power supply of the CE instrument that generates a flowthrough the packed bed capillary. In electrochromatography there is no loss of


charge: each H3O+ ion migrates under the effect of an electric field, while in liquid

chromatography, one is required working under a pressure close to 1000 bars topush the mobile phase through such a capillary column. The benefit, compared toHPLC, is the fact that in an electrically driven system the flow profile is plug-likeand therefore much more efficient than in a pressure driven system where it isparabolic (Figure 8.12).

The method requires a high-purity fused capillary filled with standard HPLCpacking materials constituted of particles that can be of very small diameters�1–3�m� or of continuous bed (monoliths) since there is no back pressure.

� Since the surface areas of microparticulate silica based packing materials aremuch greater than that of the capillary walls, a significant part of the electro-osmotic flow is generated by the remaining surface silanol groups of the stationaryphase (Figure 8.13). The packing behaves in a fashion analoguous to an untreatedinternal capillary wall. This does not apply in the case of totally base deactivatedmaterials, such as RP-18 silica which have minimal levels of residual silanol groups.

+

+ ––––

++

+

+

+

–

+

+ ––––

+++

+

–+

+ ––––

+++

+

–

+

+ ––––

+

+

+

–

+

+ ––––

+++

+

–

Retention time(s)

vEOF

–

Silica wall

++ ++ ++ ++ ++ ++ ++ ++ ++

+ + + + + + + + +

20 25 30 35 40

123

54

10 kV

15 kV

20 kV

25 kV

Packed capillary

DetectorGround

Bufferreservoir

High voltagesupply

5 kV

0 5 10 15

– – – ––– – ––

– – – ––– – ––

Figure 8.13 Schematic of a electrochromatographic installation and the representation of a smallpart of the packed capillary. The different attempts to separate a mixture of neutral compoundsby varying the voltage, verifies to a first approximation, the relation existing between voltageand velocity of electro-osmotic flow.

PROBLEMS 161

Retention time (s)

0

1 2

3 4

5

21 3

4 5Mixture:1 - Naphthalene2 - Fluoranthene3 - Benz[a]anthracene4 - Benzo[k]fluoranthene5 - Benzo[ghi]perylene

Column L = 10 cm = 6.5 cmInner Diam. 100 μmSilica 1.5 μm ODSddp: see figureFluorometric detector

1 2 3 4 5 6

.

Figure 8.14 Separation of aromatic hydrocarbons by electrochromatography. In this example theuse of a very short column and a high voltage enable the separation to be made in few seconds(for V =28 kV of a mixture of non-ionized compounds), with a good resolution. An appreciableefficiency is attained with this procedure (Amox DS et al. Anal Chem 1998, 70, 4787–92).

The stationary phase acts also with varying success as a retaining material. Non-aqueous mobile phases (for hydrophilic analytes) and untreated silica packingsmay also be used. The separation factor is very high but a change of compositionof the mobile phase or of the organic modifiers will affect the electro-osmotic flowand then the selectivity (Figure 8.14).

As in conventional liquid chromatography the plate height can be expressedusing a modified Van Deemter plate height equation.

Some problems remain, such as:

• the speed of separation is limited by the upper limit of the electro-osmoticflow velocity

• the precise control of the volume of sample introduced into the capillary

• the heat generated in the packed capillary

• the band broadening, because electrochromatography involves the use of astationary phase.

Problems

8.1 An electrophoresis analysis in free solution (CZE), calls for the use of acapillary of 32 cm and with effective length of separation 24.5 cm. The appliedvoltage is 30 kV. Under the conditions of the experiment the peak of a neutralmarker appeared upon the electropherogram at 3 min.


1. Calculate the electrophoretic mobility, �EP, of a compound whosemigration time is 2.5 min. Give the answer in precise units.

2. Calculate the diffusion coefficient under these conditions for thiscompound, remembering that the calculated plate number, N =80000.

8.2 The apparatus for an experiment using a fused silica capillary is set up. Thetotal capillary length L = 1 m while the effective capillary length l = 90 cm.The applied voltage is 30 kV. The detector is located towards the cathodeand the electrolyte is a buffer of pH 5.

In a standard solution a compound has a migration time of tm = 10min.

1. Sketch a diagram of the apparatus described.

2. From the information given, can it be deduced whether the net chargecarried by the compound is positive or negative?

3. Calculate the apparent electrophoretic mobility �app of the compound.

4. If a small molecule not carrying a charge has a migration time tm =5min, deduce the value of the electro-osmotic flux �EOS.

5. Calculate the electrophoretic mobility of the compound �EP.

6. What is the sign of the net charge carried by the compound?

7. What would happen if the fused silica capillary was coated bytrimethyl-chlorosilane?

8. Supposing that the pI of the compound was 4, what would be the signof its net charge if the pH of the electrolyte was lowered to 3?

9. Calculate the number of theoretical plates if the diffusion coefficientof the solute is D = 2 × 10−5 cm2 s−1.

10. From the relationship between the efficiency N and the diffusionD, explain why small molecules have poorer separations than largermolecules, and why for the smaller variant these separations are muchbetter when the capillary is narrower.

PROBLEMS 163

8.3 During a capillary electrophoresis experiment it is observed that if the capil-lary contains an acrylamide gel as well as an electrolyte then the speed ofmigration is slowed by the mechanical effects of filtration through the gel.This is particularly significant for larger molecules. The following relationshipcan be considered as proven:

log M = a · v + b

where a and b are two constants and M represents the molecular mass (Da)of a molecule migrating with a velocity v.

In an experiment designed to employ this relationship and in order tocalculate the molecular mass of an unknown protein, two known standardswere used; ovalbumin �M = 45000 Da� and myoglobin �M = 17 200 Da�,whose migration velocities are 15 cm min−1 and 55 cm min−1 respectively.In the same experiment, the unknown protein migrates at a velocity of325 cm min−1. Calculate its molecular mass.

8.4 Imagine that, following a capillary isoelectric focusing experiment, twopolypeptides A and B are immobilised in one section of the capillary asindicated in the figure. The isoelectric point of B is superior to that of A.

Complete the figure indicating how the pH would increase at the positiveend of the capillary while showing the orientation of the correspondingelectric field.

Flow AB

8.5 The table below lists a series of proteins along with their respective isoelectricpoints (pI). By completing the table with positive �+� or negative �−� signsor zeros (0) indicate for each protein whether the net charge will be positive,zero or negative at the three values of pH specified.

Protein pI pH = 3 pH = 74 pH = 10

insulin 5.4pepsin 1cytochrome C 10haemoglobin 7.1albumin (serum) 4.8

PART 2

Spectroscopic methods

Cu-Ka

Zn-Ka1

Zn-Kb1

As-Ka

Cd-Ka

Ag-Ka

Ag-KbSn-Ka

Sn-Kb

Cd-Kb

Sr-Ka

Sr-Ka

Sr-Kb

Ba-Ka1

Ba-Ka2

Ba-Kb1

2010 30 40keV

CuKb

166 SPECTROSCOPIC METHODS

The creators of modern colorimetry

Visual colorimetry, one of the most ancient of analytical methods was already being used inthe times of the Greeks and Romans although it began to take on a more modern scientificcharacter when, in 1729, Pierre Bouguer postulated that ‘if a given width of coloured glassabsorbs half of the light issuing from a source, then a double width will reduce the light to aquarter of its initial value’.

Some 30 years later, Jean-Henri Lambert (1728–1777) proposed the first mathematicalrelationship ‘the logarithm of the decrease in light intensity (today we would say the inverseof the transmittance) is equal to the product of the opacity of the medium times its thickness’.Finally in 1850, Auguste Beer established a relation between concentration and optical density(now called absorbance), which led to the current form of the Beer–Lambert law (also calledLambert–Beer law or even Lambert–Beer–Bouguer law).

Field of vision

Sample cell

0hx hR

0

Total reflection prism

Glass rod

Reference cell

0

Source or Mirror

Dubosc’s comparator. The observer adjusts the transmitted intensities, according to the twopathways. He can compare the quality of the colours with great precision. The bottoms of thetubes are illuminated by a reflecting surface itself lit by an annexed light source.

Amongst the different devices imagined for visual colorimetry measurements, one of the mostoriginal was described by Jules Dubosc in 1868. This instrument which remained in use until the1960s permits, due to a system of total reflecting prisms, a juxtaposition in a small circular field,of the light intensities that have travelled through two identical cells, one of which containsthe sample (concentration Cx) and the other contains a known standard (concentration CR�.The observer sees both fields with one eye, and adjusts the depths of the columns of liquid,hx of the solution to be measured and hR of the standard, until the two halves of the field areidentical in intensity. When this condition holds, the absorbances are equal. The concentrationsof the two solutions are inversely proportional to their depths, which may then be read on theinstrument.

If AR = Ax� then �hRCR = �hxCx

Thus, the concentration Cx can be deduced.This half-light comparator leads to the required concentration by taking advantage of the

Lambert–Beer law through comparison of the thicknesses crossed.

9Ultraviolet and visible absorptionspectroscopy

The absorption by matter of electromagnetic radiation in the domain rangingfrom the near ultraviolet to the very near infrared, between 180 and 1100 nm, hasbeen studied extensively. This portion of the electromagnetic spectrum, designatedas the ‘UV/Visible’ since it includes radiation perceptible to the human eye,generally yields little structural information but is very useful for quantitativemeasurements. The concentration of an analyte in solution can be determinedby measuring the absorbance at some wavelength and applying the Lambert–Beer Law. The method is known as colorimetry, considered as the workhorseof many laboratories. Colorimetry applies not only to compounds possessing anabsorption spectrum in that spectral region but equally to all those compoundswhich, following modification by specific reagents, lead to derivatives which permitabsorption measurements.

This can be achieved by a whole range of instruments, from colour comparatorsand other basic colorimetric devices to automated spectrophotometers that cancarry out multi-component analyses. Liquid chromatography and capillary elec-trophoresis have favoured the development of improved UV/Vis detectors whichreflects the current trend for acquiring chromatograms giving at the same timeinformation concerning the nature and quantification of compounds.

9.1 The UV/Vis spectral region and the origin of theabsorptions

This region of the spectrum is conventionally divided into three sub-domainstermed near UV (185–400 nm), visible (400–700 nm) and very near infrared (700–1100 nm). Most commercial spectrophotometers cover the spectral range of 185 to900 nm. The lower limit of the instrument depends upon the nature of the opticalcomponents used and of the presence, or not, along the optical pathway of air,


168 CHAPTER 9 – ULTRAVIOLET AND VISIBLE ABSORPTION SPECTROSCOPY

knowing that oxygen and water vapour absorb intensely below 190 nm. Someinstruments, on condition that they are operating in a vacuum, can attain 150 nmwith samples in the gaseous state. This is the domain of vacuum or far ultraviolet.The long-wavelength limit is usually determined by the wavelength response of thedetector in the spectrometer. High-end commercial UV/Vis spectrophotometersextend the measurable spectral range into the near infrared region as far as3300 nm.

The origin of absorption in this domain is the interaction of photons froma source with ions or molecules of the sample. When a molecule absorbs aphoton from the UV/Vis region, the corresponding energy is captured by one (orseveral) of its outermost electrons. As a consequence there occurs a modification

}

}

}

}

}

E

R1,2, n

V2

R1,2, n

V0

R1,2, n

V1

R1,2, n

V1

R1,2, n

V0

S1

S0

E

HO

hν

hν

a - radiative processb - thermal processc - internal conversion

a b

c "Singlet"

"Triplet"

LU

Singlet state Triplet state

HO and LU refer to the orbital frontier nomenclatureof “Highest Occupied” and “Lowest Unoccupied”

Electronictransitions

Ground state

Figure 9.1 Energy quantification of a molecule. Left, diagram showing different energy states ofrotation, vibration and electronic of a molecule. Each horizontal line corresponds to a distinctenergy level. The hierarchic structure is the following: between each electronic state S there liesseveral vibrational levels V, themselves also sub-divided into a collection of rotational levels R.The scale of the diagram is, of course, far from being accurate as the vibrational and rotationallevels should be closer together. On the figure, the relative distances between the three energyforms should be as their relative values, that is in the order of 1000 : 50 : 1. In condensedphases, as a result of the closeness of molecules, no instrument, regardless of its resolution canrecord a spectrum upon which are displayed the individual transitions. Right, Conventionalrepresentation of the absorption of a photon. Promotion of an electron from one occupiedorbital (HO) to an unoccupied orbital (LU) with the apparition of a singlet state giving riserapidly to a more stable triplet state. This process corresponds to a return of an excited speciesto the ground state. The transitions being quasi immediate, the distance between the atoms hasnot had enough time to change (Franck–Condon principle).

9.2 THE UV/VIS SPECTRUM 169

of its electronic energy �Eelec�, a component of the total mechanical energy of themolecule along with its energy of rotation �Erot� and its energy of vibration �Evib�(expression 9.1).

A modification of Eelec will result in alterations for both Erot and Evib resultingin a vast collection of possible transitions obtained in all three cases (Figure 9.1),and since the polarities of the bonds within the molecules will be disturbed theirspectra are given the generic name of charge transfer spectra.

�Etot = �Erot + �Evib + �Eelec (9.1)

with �Eelec > �Evib > �Erot.

� All observed spectra are obtained from a sample containing an huge number ofmolecules or other individual species which are not all in the same energy state.The resulting graph corresponds to a band type curve that envelops the individualtransitions of the present species.

The energy captured during the course of photon absorption can be releasedthrough a variety of processes that occur concurrently with emission of a photon(Figure 9.1c). Phosphorescence and fluorescence are transformations of this kind,which are exploited in other analytical methods (cf. Chapter 11).

9.2 The UV/Vis spectrum

UV/Vis spectrometers collate the data over the required range and generate thespectrum of the compound under analysis as a graph representing the transmit-tance (or the absorbance) as a function of wavelength along the abscissa, given innanometres, the recommended unit in this region, rather than in cm−1 (Figure 9.2).

In spectroscopy, the transmittance T is a measure of the attenuation of a beamof monochromatic light based upon the comparison between the intensities of thetransmitted light (I) and the incident light �I0� according to whether the sampleis placed, or not, in the optical pathway between the source and the detector.T is expressed as a fraction or a percentage:

T = I

I0

(9.2)

or

%T = I

I0

× 100

The absorbance (old name optical density) is defined by:

A = − log T (9.3)

The recorded spectra of compounds in the condensed phase, whether pure or insolution, generally present absorption bands that are both few and broad, while


Abs

orba

nce

Wavenumber (cm–1)

a Benzene in solution

a

b Benzene vapour

b

c

c Iodine vapour

Wavelength (nm)

252.5253.5

18628 1862518627 18626 18624 186230

50

100

%T

536.83 nm 536.97 nm

Figure 9.2 Three different aspects of UV/Vis spectra. Spectra of benzene (a) in solution (a bandspectrum); (b) in the vapour state (spectrum presenting a fine structure); (c) an expansion ofa section from the high resolution (0.14 nm total interval) line spectrum of iodine vapour. Thespectrum of benzene vapour, obtained from a drop of this compound, deposited in a silicaglass cuvette of 1 cm optical path, provides an excellent test to evaluate the resolution of anUV-spectrophotometer.

those spectra obtained from samples in the gas state and maintained under a weakpressure yield spectra of detailed ‘fine structure’ (Figure 9.2). For compounds ofsimple atomic composition, providing the spectrometer possesses a high enoughresolution, the fundamental transitions appear as if isolated. In extreme situationssuch as these, the positions of the absorptions are recorded in cm−1, a unit betteradapted for a precise pointing than the nm (the calculation reveals that there are111 cm−1 between 300 and 301 nm).

9.3 ELECTRONIC TRANSITIONS OF ORGANIC COMPOUNDS 171

9.3 Electronic transitions of organic compounds

Organic compounds represent the majority of the studies made in the UV/Vis. Theobserved transitions involve electrons engaged in � or � or non-bonding n electronorbitals of light atoms such as H, C, N, O (Figure 9.3). Where possible the characterof each absorption band will be indicated in relation to the molecular orbitals (MO)concerned and the molar absorption coefficient ��Lmol−1cm−1

� calculated at thewavelength corresponding to the maximum of the absorption band.

9.3.1 � → �∗ transition

This transition appears in the far UV since the promotion of an electron from a� bonding MO to a �∗ anti-bonding MO requires a significant energy. This is thereason for saturated hydrocarbons that only contain this type of bonding beingtransparent in the near UV.

Example: hexane (gas state): �max = 135nm�� = 10000�.Cyclohexane and heptane are used as solvents in the near UV. At 200 nm

the absorbance of a 1 cm thickness of heptane is equal to 1. Unfortunately, thesolvation power of these solvents is insufficient to dissolve many polar compounds.

Similarly, the transparency of water in the near UV (A = 001 for l = 1 cm, at� = 190nm) is due to the fact there can only be transitions � → �∗ and n → �∗

in this compound.

9.3.2 n → �∗ transition

The promotion of an n electron from an atom of O, N, S, Cl to an MO �∗ leadsto a transition of moderate intensity located around 180 nm for alcohols, near

π∗

π

σ∗

σ

n π∗

π π∗

n σ∗

σ∗σ

(if unsaturated)

w = Weak transitions = Strong transition

200 nm 400 nm

E

(w)

(s)

(s)

n σ∗

π π∗

n π∗

n

σ∗σ

(w)

Wavelengths

Figure 9.3 Comparison of the transitions met most frequently with simple organic compounds.The four types of transition are united on a single energy diagram in order to situate them withrespect to each other and to correlate them with the corresponding spectral ranges concerned.


hνNH2 NH3NH2 Aniline

HXX–

Aniline

Figure 9.4 Transition n→�∗ of aniline (a primary amine). This transition corresponds to anincrease in the ‘weight’ of the mesomeric form. The absorption peak of aniline representing thistransition would disappear if one equivalent of a protonic acid of type HX is added, since theformation of an ammonium salt would immobilize the lone pair of the nitrogen atom necessaryfor this transition (see the intermediate between the brackets).

190 nm for ethers or halogen derivatives and in the region of 220 nm for amines(Figure 9.4).

Examples: methanol: �max = 183nm�� = 50� ether: �max = 190nm�� = 2000�ethylamine: �max = 210nm�� = 800�; 1-chlorobutane: �max = 179nm.

9.3.3 n → �∗ Transition

This transition of low intensity results from the passage of an n electron (engagedin a non-bonding MO) to an anti-bonding �∗ orbital. This transition is usuallyobserved in molecules containing a hetero atom carrying lone electron pairs as partof an unsaturated system. The best known is that corresponding to the carbonylband, easily observed at around 270 to 295 nm. The molar absorption coefficientfor this band is weak.

Example: ethanal: � = 293nm�� = 12, with ethanol as solvent).

9.3.4 � → �∗ Transition

Compounds possessing an isolated ethylenic double bond reveal a strong absorp-tion band around 170 nm. The precise position depends upon the presence ofheteroatom substituents.

Example: ethylene: �max = 165nm�� = 16000�.A compound that is transparent in a given spectral range of the near UV when it

is isolated, can become absorbing if it interact with a species through a mechanismof type donor–acceptor (D-A). This phenomenon is linked to the passage of anelectron from a bonding orbital of the donor (which becomes a radical cation)towards a vacant orbital of the acceptor (which becomes a radical anion) of anattainable energy level (Figure 9.5). The position of the absorption band in thevisible part of the spectrum is a function of the ionization potential of the donorand of the electron affinity of the acceptor; the value of � is, in general, very large.

9.4 CHROMOPHORE GROUPS 173

Donor DonorAcceptor AcceptorE E E

LU LU

HO HO

LU LU

HO HO

Juxtaposition of D and A Appearance of a D+/A– complex

hν1

hν2hν3

+ –

Figure 9.5 Energy diagram for a donor/acceptor interaction. The excited state is supposed tobe essentially in the ionic form

9.3.5 d → d transition.

Numerous inorganic salts containing electrons engaged in d orbitals are respon-sible for transitions of weak absorption located in the visible region. These tran-sitions are generally responsible for their colours. That is why the solutions ofmetallic salts of titanium Ti�H2O�6�

3+ or of copper Cu�H2O�6�2+ are blue, while

potassium permanganate yields violet solutions, and so on.

9.4 Chromophore groups

The functional groups of organic compounds (ketones, amines, nitrogen deriva-tives, etc.), responsible for absorption in UV/Vis are called chromophores(Table 9.1). A species formed from a carbon skeleton transparent in thenear UV on which are attached one or several chromophores constitutes achromogene.

• Isolated chromophores: for a series of molecules having the same chromophore,the position and the intensity of the absorption bands remain constant. Whena molecule possesses several isolated chromophores, that is, which do not

Table 9.1 Characteristic chromophores of some nitrogen-containinggroups

Name Chromophore �max �nm� �max�Lmol−1cm−1�

Amine −NH2 195 3000Oxime = NOH 190 5000Nitro −NO2 210 3000Nitrite −ONO 230 1500Nitrate −ONO2 270 12Nitroso −N = O 300 100


Table 9.2 Correlation table in UV/Visible spectroscopy. Fieser–Woodward–Scottrules for the calculation of the position of the absorption maxima for enones anddienones (margin 3 nm).

Type of structure concerned:(chemical formula)

solvent: methanol or ethanol

Basic structure(chemical formula)

open chain or ring of 6 C(ring of 5 C: 202 nm)Increments:

- each additional conjugated double bond: 30 nm- exocyclic character of C=C double bond: 5 nm- dienic homoannular character: 39 nm- for each substituent, add (in nm): positions

Solvent increments:- water 30 nm- chloroform- ether - cyclohexane

+8 nm–1 nm–7 nm

–11 nm

C C C CC CCC

OOX X

-Cl 15 12-Br 25 30

-N(R)2 95

alkyl 10 12 18 18

-OH 35 30 50-O-alkyl 35 30 17 31-O-acyl 6 6 6 6

α β γ δ

interact with each other because they are separated by at least two singlebonds in the skeleton, then the overlapping of the effects of each individualchromophore is observed.

• Conjugated chromophore systems: when the chromophores interact with eachother the absorption spectrum is displaced towards longer wavelengths(bathochromic effect) with an increase in the absorption intensity (hyper-chromic effect). A particular case is that of molecules with conjugated systems,that is, organic structures containing several adjacent to one another unsat-urated chromophores (i.e. separated by a single bond). The spectrum isthen strongly disrupted with respect to the overlapping effects of isolatedchromophores. The greater the number of carbon atoms upon which theconjugated system is extended, the greater the reduction in the differencebetween energy levels (Table 9.2). This results in a very large bathochromiceffect (Figure 9.6).

9.5 Solvent effects: solvatochromism

Each solvent has its own characteristic polarity. Since it is known that all electronictransitions modify the charge distribution of the compound in solution, it is obviousthat the position and intensity of the absorption bands will vary a little with thenature of the solvent used. The nature of the solvent/solute interactions are a greaterindication of the type of transition. Two contrasting effects can be distinguished.

9.5 SOLVENT EFFECTS: SOLVATOCHROMISM 175

400

448

425

480

Abs

orba

nce

in h

exan

e

Log(

Abs

orba

nce)

Wavelength (nm)

4.4

4.5

4.6

4.7

4.8

4.9

5

5.1

5.2

150 200 250 300 350 400

H

H

n

500450nm

β-carotene (all trans)

β-carotene

Figure 9.6 The effect of several conjugated double bonds upon the position of the absorptionmaxima of the transition � → �∗ for several conjugated polyenes. Values of �max for a family ofE-disubstituted conjugated polyenes which differ between them by the number of conjugateddouble bonds. This effect is at the origin of the colour in numerous natural compounds whosestructural formulae present extended conjugated chromophores. An example is the orangecolour of ‘all-trans’ �-carotene above which arises from the presence of eleven conjugateddouble bonds ��max = 425 448 and 475 nm in hexane). The broader the delocalization of theelectrons the greater will be the bathochromic effect. Aromatic compounds lead to spectra morecomplex than those of ethylenics, the transitions � → �∗ being at the origin of ‘fine structure’.

9.5.1 Hypsochromic effect (the ‘blue shift’)

If the chromophore responsible for the observed transition is more polar in itsfundamental state than when it is excited, then a polar solvent will stabilize,by solvation, the form prior to absorption of the photon. Molecules of solventwill be clustered around the solute because of electrostatic effects. More energywould therefore be required to excite the electronic transition concerned, causinga displacement of the absorption maxima to shorter wavelengths than would occurin a non-polar solvent. This is the hypsochromic effect (Figure 9.7).

This is rather like the n → �∗ transition of the ketone carbonyl in solution.The C+−O− form (characterized by its dipolar moment �) will be more andmore stabilized as the solvent becomes more polar. The excited state being rapidlyattained, the solvent shell surrounding the carbonyl has no time to reorient itselfand bring about stabilization following absorption of the photon. This same effectis observed for the n → �∗ transition and is accompanied by a variation of thecoefficient �.


Bathochromic effect

“blue shift”

“red shift”

Hypsochromic effect

220 260 300 (nm) 340 380

log ε

O

C

2

3

4

n π*

nπ

CyclohexaneEthanol

E

π π* π* π*

hν3 hν4

hν3

hν2 hν1

hν1 hν2

hν4

Solvent

E

E

no polar polar no polar polarSolvent

Figure 9.7 Spectra of benzophenone in cyclohexane (1) and in ethanol (2). Observed here withtwo different solvents and upon two types of transitions are the bathochromic and hypsochromiceffects.

9.5.2 Bathochromic effect (the ‘red shift’)

For less polar compounds the solvent effect is weak. However, if the dipole momentof the chromophore increases during the transition, the final state will be moresolvated. A polar solvent can thus stabilise the excited form, which favours thetransition: a displacement is observed towards longer wavelengths when comparedwith the spectra obtained with a non-polar solvent. This is the bathchromic effect(Figure 9.7). For example, this is the case for the � → �∗ transition of ethylenichydrocarbons of which the double bond is only weakly polar.

9.5.3 Effect of pH

The pH of the solvent in which the solute is dissolved can have an importanteffect on the spectrum. Amongst the compounds that present this effect in aspectacular fashion are chemical indicator strips, whose change in colour is usedduring acidimetric measurements (Figure 9.8). Equivalent points can be locatedby this methodology.

9.6 Fieser–Woodward rules

Structural analysis from electronic spectra is a fairly vague exercise, in the sensethat the relative simplicity of the spectrum has for corollary a poor yield ofinformation. In the 1940s, however, before the development of more powerfultechniques of identification, now taken for granted, UV/Vis spectroscopy wasemployed for this purpose. Studies of spectra for a large number of moleculesled to the establishment of a correlation between structures and positions of

9.6 FIESER–WOODWARD RULES 177

pH

240

0.2

0.4

320400

480560Wavelength (nm)

10.5

9.0

7.5

6

pH > 8

OO–

O–

O

O

O

OHHO

Abs. Abs.

Figure 9.8 The effect of pH upon a solution of phenolphthalein. This compound is not colouredat pH values less than 8 though it is bright pink for those greater than 9.5. The graph presentedhere in 3D perspective reveals that for acid pH there is no absorption in the visible region ofthe spectrum. In contrast, absorptions towards 500 nm appear when the pH becomes alkaline,which are responsible for the well-known colour of the compound. Notable in this example isthe modification in the chemical bonding, which is pH dependent.

the absorption maxima. The best known of these are the empirical rules dueto Fieser, Woodward and Scott, which concern unsaturated carbonyl, dienes orsteroids compounds. The table presents in the form of increments to �max a varietyof factors and structural features affecting the position of the absorption band� → �∗ for these conjugated systems (Table 9.2).

There is good agreement between the calculated values and those derived fromexperiment for the four examples displayed in Figure 9.9.

CO2H

O

234234

217215

386 nm385 nm

231229

λmax Meas.Calc.

Figure 9.9 Comparison between calculated and experimental values for some unsaturated organiccompounds. The calculations were made from values given in Table 9.2


9.7 Instrumentation in the UV/Visible

A spectrophotometer is designed around three fundamental modules: the source,the dispersive system (combined in a monochomator), which constitute the opticalsection and the detection system (Figure 9.10). These components are typicallyintegrated in a unique framework to make spectrometers for chemical analysis. Asample compartment is inserted into the optical path either before or after thedispersive system depending upon the design of the instrument.

Certain instruments are reserved for routine analyses for which a high resolutionis not required. Numerous compounds in solution lead to spectra lacking infine bands. However it is essential that these instruments are able to give precisequantitative results to within several units of absorbance.

9.7.1 Light sources

All spectrometers require a light source. More than one type of source can be usedin the same instrument which automatically swap lamps when scanning betweenthe UV and visible regions:

• for the visible region of the spectrum, an incandescent lamp fitted with atungsten filament housed in a silica glass;

• for the UV region a deuterium arc lamp working under a slight pressure tomaintain an emission continuum (<350nm�;

• alternatively, for the entire region 200 to 1100 nm, a xenon arc lamp can beused for routine apparatuses.

DetectorMonochromator

Single or double beam, normal optic sequential spectrometer

Single beam, reverse optic simultaneous spectrometer

Source

Sample solution

Sample solution

Dispersive systemDiode arraydetector

Source

Figure 9.10 Instrumentation in the UV/Vis. Two optical schemes are displayed which generatea spectrum by following two different procedures. In the first design on which the majorityof instruments are based, the spectrum is obtained in a sequential manner as a function oftime (one wavelength after another). In the second, the detector ‘sees’ all of the wavelengthssimultaneously.

9.7 INSTRUMENTATION IN THE UV/VISIBLE 179

� The deuterium discharge lamp contains two electrodes bathed in an atmosphereof deuterium (D2 is preferred to hydrogen H2, for technical reasons). Between theelectrodes a metallic screen is placed which is pierced with a circular hole of approxi-mately 1 mm diameter (Figure 9.11). The migration of the electrons toward the anodecreates a discharge of current generating an intense arc at this hole, which is in frontof the anode. Subjected to this electron bombardment the molecules of deuteriumD2 dissociate, emitting a continuum of photons over the wavelengths range between160 and 500 nm.

9.7.2 Dispersive systems and monochromators

Sequential instruments

The light emitted by the source is dispersed through either a planar orconcave grating which forms part of a monochromator assembly. This devicepermits the extraction of a narrow interval of the emission spectrum. Thewavelength or more precisely the width of the spectral band, which is afunction of the slit width, can be varied gradually by pivoting the grating(Figure 9.12). Optical paths with long focal lengths (0.2 to 0.5 m) yield the bestresolution.

Simultaneous instruments

This category of instrument functions according to the spectrograph prin-ciple. The light beam is diffracted after travelling through the measuring cell(Figure 9.13).

9.7.3 Detectors

The detector converts the intensity of the light reaching it to an electricalsignal. It is by nature a single channel device. Two types of detector areused, either a photomultiplier tube or a semiconductor (charge transfer devicesor silicon photodiodes). For both of which the sensitivity depends upon thewavelength.

For ‘simultaneous’ instruments which do not possess a monochromator but adispersive system, the light intensity at all wavelengths is measured practically atthe same instant by aligning a large number of detectors in the form of a diodearray (Figure 9.13). The photoelectric threshold, in the order of 1 eV, extends therange of detection up to 11�m.

The efficiency of the photomultiplier tube – a very sensitive device whoselinearity of response reaches seven decades – depends upon the yield at the


iIrra

dian

ce a

t 0.5

miIr

radi

ance

at 0

.5 m

200 300 400 500 600 700

Semi-log display of a deuterium lamp

Semi-log displays of arc xenon lamp and quartz tungsten halogen (QTH) lamps

500200 800 1100 1400 1700

10

100

1000

1

0,1

10

100

1000

1

0,1

Diagram of a deuterium lamp

486 nm

656.1 nm

Wavelength (nm)

Wavelength (nm)

Lamp, view from above1 - Silica glass envelope2 - Filament (cathode)3 - Metal screen4 - Anode

Connections

+

–

hν

200–400V =

12

3

4

a few volts ~

xenon lines

Figure 9.11 Emission spectra of the different types of sources in UV/Vis. A logarithmic scaleaccounts for the big differences of light intensity according to the wavelengths, notably forfilamentless lamps. Below left and middle, general view of a lamp and that seen from above(reproduced courtesy of Oriel). Schematic presenting the circuit details for the lamp. The lampis booted with a voltage of between 3 to 400 V. The anode is a molybdenum plate while thecathode is a filament of metallic oxide able of emitting electrons and connected to an electricalsupply. The emission peaks of deuterium at 486 and 656.1 nm are often used to calibrate thespectrometer wavelength scale.

9.8 UV/VIS SPECTROPHOTOMETERS 181

(b) Czerny-Turner assembly

Light pathway in the concave grating assembly

(a) Ebert assembly

(c) Concave grating assembly

Grating

Grating

Grating

M2

M4M3

F2

F1

M1

M2

M3

F2

F1

M1

M1 F2

F1

M2

GC

Figure 9.12 Monochromator gratings. (a) Ebert assembly incorporating a single concave spher-ical mirror M3. Able to compensate for aberrations this monochromator gives excellent imagequality. (b) Of similar design to Ebert the Czerny–Turner assembly contains two sphericalconcave mirrors M3 and M4. (c) The concave grating Rc in this design permits both dispersionand focussing of the radiation. The spectral bandwidth of these monochromators depends uponthe width of the entrance F1 and the exit F2 slits, respectively.

photocathode, which varies with the wavelength (e.g. 01 e−/photon at 750 nm),and on the signal gain provided by the cascade of dynodes (e.g. a gain of 6 × 105).With such values the impact of 10 000 photons/s produces a current of 0.1 nA.For a photomultiplier it is difficult, just as it would be for the eye to compare twolight intensities with precision, one arising from the reference beam and the otherfrom the sample, when they are quite different. This is why it is desirable thatthe absorbance of the solutions does not exceed 1 (see equally Section 9.14). Onthe other hand, for an instrument whose stray light is of 0.01 per cent (measuredin percentage transmittance), an increase in solution concentration produces nosignificant variation in the signal beyond than 4 units of absorbance.

9.8 UV/Vis spectrophotometers

UV/Vis spectrometers are classified into three optical designs: a fixed spectrometerwith a single light beam and sample holder; a scanning spectrometer with double


T

1 2

hνhν

Electrode

–

Si type nnp+ +

Depletion zone

Figure 9.13 Silicon photodiode (PIN) and diode array (CCD detectors – charged coupled device).Each diode, of rectangular shape �15×25�m�, is associated with a charged capacitor. Under theimpact of photons the diode becomes a conductor and progressively discharges the capacitor.This diode (PIN type) has a large intrinsic region sandwiched between P-doped and N-dopedsemiconducting regions. Photons absorbed in this region create electron-hole pairs that arethen separated by an electric field, thus generating an electric current in a load circuit. Thevalue of the residual charge of each of the capacitors depends upon the number of the photonsreceived. This is measured in a sequential fashion by the electronic circuits (1 and 2). Thecapacitors are recharged periodically. This is in contrast to the photomultiplier tube which givesan instantaneous measurement of intensity in watts, while the diode leads to an indication ofthe energy emitted in joules over a time interval. The sensitivity, linearity and the dynamicrange of response of the photomultiplier tube are excellent.

light beams and two sample holders for automatic measurement of absorbance;and a non-scanning spectrometer with an array detector for simultaneous measure-ment of multiple wavelengths.

9.8.1 Single-beam monochannel optical spectrometers

Many routine measurements are conducted at fixed wavelengths by basic photome-ters fitted with interchangeable interference filters or simple grating monochro-mators. In single-beam instruments, obtaining a spectrum requires measuring thetransmittance of the sample and of the solvent at each wavelength. A control corres-ponding to the solventaloneora solutioncontaining the reagentsof themeasurement(but without the compound to be measured, an analytical blank), is first placed in theoptical path, then is replaced by the solution prepared from the sample of unknownconcentration. These instruments sometimes have a built-in electronic compensa-tion arrangement for variations in light source intensity (Figure 9.14) known as asplitbeam. A part of the light beam is diverted before it reaches the sample permit-ting the stabilization of the source intensity (this is not a true reference beam). Theseinstruments yield absorbance and led to the analyte concentration.

9.8.2 Array-detector spectrophotometers

This type of instrument resembles a spectrograph closely since it allows the simul-taneous recording of all wavelengths of the spectrum by using an array of up to


W lamp (Vis.)

D2 lamp (UV)

Photodiode # 1

Photodiode # 2Reference

SampleFilter

Mirror

M1 2

3

Entry slit

Exit slit

Concavegrating

Semi-transparentmirror

Calculationof the transmittance(or absorbance)

4

Figure 9.14 Simplified scheme of the optical path of a simple beam, sequential mode spectropho-tometer. 1. Two co-existing sources, though only one is selected for the measurement. 2. Themonochromator selects the measurement wavelength. 3. The measuring cell containing eithersample or control blank is placed in the optical path. 4 and 5. Diode detector and control diode.

a few thousands of miniaturized photodiodes (Figure 9.15). Array-detector spec-trophotometers allow rapid recording of absorption spectra, each diode measuringthe light intensity over a small interval of wavelength. The resolution power ofthese diode-array instruments, without a monochromator, is limited by the size ofthe diodes. These instruments use only a single light beam, so a reference spectrumis recorded and stored in memory to produce transmittance or absorbance spectraafter recording the sample spectrum.

9.8.3 Double-beam scanning spectrometer

The double-beam design greatly simplifies the process of the single-beaminstrument by measuring the transmittance of the sample and solvent almostsimultaneously. One beam passes through the sample while the other passesthrough the reference solution. Most spectrometers use one (or two) mirroredrotating chopper wheel to alternately direct the light beam through the sampleand reference cells. This permits the detector to compare the two intensities trans-mitted by reference or sample solutions for the same wavelength (Figure 9.16).The amplification of the modulated signal allows the elimination, in large part,of the stray light. The electronic circuit adjusts the sensitivity of the photomulti-plier tube as the inverse with respect to the light intensity it receives. A simplerset-up is based on the use of semi-transparent mirror and two connected photo-diodes. The signal corresponds to the potential difference required to maintain aconstant detector response (principle of a feedback system). These instruments arecharacterized by a fast scanning speed (30 nm/s) and the capability of measuringabsorbances to within just a small number of units.


Grating

Sample cuvetor flow cell

Movable shutter

Achromatic lenses

Source (lamp)

Photodiodearray

500 nm190 nm25 mm

Figure 9.15 Schematics of a single beam spectrophotometer illustrating the simultaneous mode(spectrometer with diode array) and miniature UV/Vis spectrophotometers. Above: the shutter, theonly mobile piece in this assembly serves in the reduction of the background noise or darkcurrent produced when no light reaches the photodiodes. All wavelengths pass through thesample. These spectrometers use photodiode arrays (PDAs) or charge-coupled devices (CCDs)as the detector. The spectral range of these array detectors is typically 200 to 1000 nm. Withthis inverted optical design the sample compartment can be exposed to the external light. Theseinstruments are used mainly as detectors in liquid chromatography (cf. Section 3.7). Below:examples of miniature spectrometers whose dispersive system and detector are integrated into acircuit board, which can be inserted into a personal computer. An optical fibre transmits the lightfrom the source/sample cell situated at a distance (reproduced courtesy of Ocean Optics Europe).

� Wavelength calibration in UV/Vis. To provide accurate measurements, UV/Vis.spectrometers must be accurately calibrated – with regard to both their intensity(transmittance) and location (wavelength) axes. To calibrate the wavelength scaleof the spectrometer a solution of a few percent of holmium oxide (Ho2O3) in diluteperchloric acid is used. This solution has numerous narrow absorption bands welldistributed over the wavelengths for which the different maxima are known. Thevalues depend little upon the spectral bandwidth. In fact, the absorption bands ofthe spectrum are not symmetrical so that the spectral bandwidth selected for visu-alization has an influence upon the energy reaching the detector which has in turnrepercussions on the intensity of the signal and finally upon the recorded spectrum,e.g. in passing from a slit size 0.1 nm to 3 nm, the maximum at 536.47 nm is displacedto 537.50 nm.


Assembly with photomultiplier Reference

Sample

Sample

PhotomultiplierRotating mirror (detail)

Cells

Cells

Rotating mirrors

Monochromator

Monochromator

Source

Source

Assembly with two photodiodes

Photodiodes

Semi-transparentmirror

Reference

Figure 9.16 Optical path from the exit of the monochromator to the detector for two doublebeam instruments, (a model with two rotating mirrors and a model with a semi-transparentmirror). The arrangement of the apparatus with rotating mirrors is similar to that of IRspectrophotometers apart from the fact that the light beam issuing from the source passes firstthrough the monochromator before it hits the sample. In this way the photolytic reactionswhich could occur owing to an overexposure to the total radiation issued from the sourceare minimized. A more compact and simple optical assembly with a single beam associatedwith two detectors. A semi-transparent and fixed mirror replaces the delicate mechanism ofsynchronized, rotating mirrors.

Double beam spectrophotometers allow differential measurements to bemade between the sample and the analytical blank. They are preferable to thesingle beam instruments for cloudy solutions. The bandwidth of high perfor-mance instruments can be as small as 0.01 nm. For routine measurements such asmonitoring a compound on a production line, an immersion probe is employed.Placed in the sample compartment of the apparatus this accessory contains twofibre-optics, one to conduct the light to the sample and another to recover itafter absorption in the media studied. Two types exist: by transmission for clearsolutions and by attenuated total reflection (ATR) for very absorbent solutions(Figure 9.17).

� Fluorescent compounds. When the compound studied is fluorescent, the absorp-tion spectrum is less intense because the re-emitted light gives, as a conse-quence, an inaccurate value for the true absorbed light. Observed using anassembly of reversed optics, the fluorescence of the sample (exposed to the total


Source Monochromator

Reference

Sample

Sample

“Optrode”

Detector

Sapphire prism

221 1

1 - Input fibre2 - Output fibre 1 - Input optic fibre

2 - Output optic fibre

Thicknesstraversed

Beampenetration

Figure 9.17 The principle of a spectrophotometer fitted with an immersion probe. Monochro-matic light issuing from a spectrophotometer is guided towards an immersion cell and thenreturned to the detector. The route is confined by a fibre optic. Left: transmission probe.Right: ATR probe; the sapphire prism has a refraction index greater than that of the solution.The schematic shows three reflections of the beam and its penetration into the solution (seeexplanation in Chapter 10, Section 10.9.3).

radiation of the source) reduces the absorbance in the region of the spectrumwhere the emission is situated. Alternatively, with a traditional optical assembly,the fluorescence appears when the monochromator selects the region corres-ponding to the excitation: the absorbance will be less intense in the regionwhere compound fluoresces. However, the problem should not be exaggeratedas the fluorescence is emitted in all directions and the photons taking the opticalpath for the absorption experiment constitute a very small part of the emittedlight.

9.9 Quantitative analysis: laws of molecular absorption

9.9.1 Lambert–Beer law

The UV/Vis domain has been widely exploited in quantitative analysis andthe visible region for a particularly long time. The measurements are based uponthe Lambert–Beer law which, under certain conditions, links the absorption of thelight to the concentration of a compound in solution.

The origins of this law are found in the work of the French mathematicianLambert who laid down the basis for photometry in the eighteenth century. LaterBeer, a German physicist of the following century, proposed a law, which led tothe calculation of the quantity of light transmitted through a given thickness of acompound in solution in a non-absorbing matrix.

9.9 QUANTITATIVE ANALYSIS: LAWS OF MOLECULAR ABSORPTION 187

The result was the Lambert–Beer law which is presented here in its current form:

A = ��lC (9.4)

A represents the absorbance, an optical parameter without dimension accessiblewith a spectrophotometer, l is the thickness (in cm) of the solution throughwhich the incident light is passed, C the molar concentration and �� the molarabsorption coefficient �L mol−1 cm−1

� at wavelength �, at which the measurementis made. This parameter, also called the molar absorptivity, is characteristic of thecompound being analysed and depends among other things upon the temperatureand the nature of the solvent. Generally its value is given at the wavelength of themaximum absorption. This can vary over a wide range going from zero to over200 000.

According to Lambert’s hypothesis, the intensity I of monochromatic radiationis decreased by dI (negative value) after passing through a thickness dx of amaterial whose absorption coefficient is k for the wavelength x chosen (Figure 9.18),being:

−dI

dx= kIx (9.5)

In calling I0 the light intensity of the incident radiation before it passes through themedium of thickness l, that has an absorption coefficient k, expression 9.5 can bewritten in integrated form giving the transmitted intensity I (Equations 9.6 to 9.8):

lnIx�II0

= −k x�l0 (9.6)

lnI

I0

= −k · l (9.7)

I = I0e−kl (9.8)

In 1850, Beer proposed the general expression 9.9 for the case of a solutionof low concentration dissolved in a transparent medium (non-absorbing), bywriting that k is proportional to the molar concentration C of this compound(Figure 9.19):

k = k′ · C (9.9)

By replacing k with k′C in expression 9.7 a new relation is obtained which is betterknown in the form of expression 9.4, in which the absorbance A is represented byone of the comparable expressions:

A = logI0

I or A = log

1

Tor A = log

100

T%or A = 2 − log T% (9.10)

The Lambert–Beer law, considered in this approach as a postulate, has been thesubject of different interpretations and demonstrations of statistical hypotheses,


0102030405060708090

100

0 0.2 0.4 0.6 0.8 1 1.2Thickness traversed

Material with coefficient k

%T = 100 (I /I0)

0 x

dx

I

k

IxI0(lx – dl)

l

Figure 9.18 Absorption of the light by a homogeneous material and representation of percentagetransmittance as a function of the material’s thickness. The light reaching the sample can bereflected, diffused, transmitted or absorbed. Here only this last fraction is taken into account.

0

0.51

1.52

2.53

3.54

4.55

0 100 200 300 nm 400

Concentration (mg/L)

Absorbanceλ = 525 nm

KMnO4 in water

Abs5.000

4.000

3.000

2.000

1.000

0.000

–1.000220.00 300.00 400.00 500.00 600.00 700.00

nm

325 mg/l

260

195

130

65

Figure 9.19 Illustration of the Lambert–Beer law. Spectra of aqueous solutions of increasingconcentration in potassium permanganate. Graph of the corresponding absorbances measuredat 525 nm showing the linear growth of this parameter.

kinetics or simple logic. k may be related to � , absorption cross-section(cm2/molecule) and n, number density (molecules/mL): k = �n.

This law, which concerns only that fraction of the light absorbed can be verifiedby application of the following conditions:

• the light used must be monochromatic

• the concentrations must be low

• the solution must be neither fluorescent or heterogeneous

• the solute must not undergo to photochemical transformations

• the solute must not undertake variable associations with the solvent.

9.9 QUANTITATIVE ANALYSIS: LAWS OF MOLECULAR ABSORPTION 189

In general, when the absorbance is to be measured at a single wavelength, theabsorption maximum is chosen. In order that the absorbance reflects the concen-tration, it is required that the spectral band �� reaching the detector and pre-selected by the instrument parameter called bandwidth, will be much narrower(10 times) than the width of the absorption band measured at mid-height (seewavelength calibration in Section 9.8.3).

9.9.2 Additivity of absorbances

The Lambert–Beer law is additive (Figure 9.20). This means that if the absorbanceA is measured for a mixture of two compounds, 1 and 2 in a solvent and placedin a cuvette of thickness l the same total absorbance (expression 9.11) will beobtained if the light had successively passed through two cuvettes of thickness l,placed one after the other, one containing compound 1 (Abs. A1) and the othercompound 2 (Abs. A2). Of course the concentrations and the solvent must remainthe same as for the initial mixture (compound 1 is labelled 1 and compound 2 islabelled 2):

Experiment 1: A = l��1C1 + �2C2�

Experiment 2: A1 = l�1C1 and A2 = l�2C2

A = A1 + A2 (9.11)

This principle is illustrated by the study of isobestic points. Consider acompound A, which is transformed by a reaction of first order to compound B.Assume that the absorption spectra of A and B recorded separately in the samesolvent and at the same concentration, cross over at a point I when one is super-imposed upon the other (Figure 9.21). Consequently, for the wavelength of point I,the absorbances of the two solutions are the same and by corollary the coefficients�A and �B are equal ��A =�B =��. In this transformation, compound A is initially

C2C1 A = A1 + A2

Source

C1 + C2

ll Detector Detector

SourceA1 A2

Abs. A Abs. A

l

Figure 9.20 Additive nature of absorbances. For all wavelengths, the absorbance of a mixtureis equal to the sum of the absorbances of each component within the mixture (assuming thesame molar concentrations in the two experiments).


Abs

orba

nce

Wavelength (nm)280 350

Figure 9.21 Isobestic point. Alkaline hydrolysis of methyl salicylate at 25 �C. Superimpositionof the successive spectra recorded between 280 and 350 nm at 10 min intervals. At isobesticwavelength, the absorbance is invariant.

alone and ultimately compound B is also pure. For all intermediate solutions, theglobal concentration for mixtures of A and B does not change �CA + CB = C ste),which can be given by the following expression:

AI = �AlCA + �BlCB = �l�CA + CB� (9.12)

All of the spectra of the various mixtures of A + B formed over time will pass bythe point I, called the isobestic point, where the absorbance A will always be ofthe same value.

This network of concurrent curves is observed when studying coloured indica-tors as a function of pH, or kinetic studies of particular reactions (Figure 9.21).The isobestic point is useful to measure the total concentration of two species inequilibrium, i.e. an isomerization reaction.

9.10 Methods in quantitative analysis

When a compound does not absorb light, it can nevertheless become the subjectof a photometric measurement if it can be transformed beforehand to a derivativethat has an exploitable chromophore. Using this method it becomes possible toquantify all kinds of chemical species that have no significant absorption becauseit is very weak, or because it lies in a region of the spectrum where co-exists otherabsorptions which interfere. To counteract this, the measurement of absorbanceis preceded by a chemical transformation which must be specific, total, rapid,

9.10 METHODS IN QUANTITATIVE ANALYSIS 191

reproducible and lead to a stable derivative in solution, that is UV/Vis absorbing.This is the principle of colorimetric tests.

The term colorimetry arose from the statement that initial measurements inthis field, well before the invention of the spectrophotometer, were carried outwith natural light (white light) and by direct visual comparison of the colorationof the sample with that of a control of known concentration. Apart from the eye,no other particular instrumentation was used.

The two situations that can be encountered most frequently are:

• The analyte to be measured is present in a matrix whose other constituents absorbalso in the same spectral range: the direct measurement of the absorptiondue solely to this compound is therefore impossible (Figure 9.22, curve a).To overcome this difficulty, the compound is transformed specifically into aderivative whose absorption curve is situated in a region free from interferenceby the matrix (Figure 9.22, curve b).

• The analyte to be measured has no exploitable chromophore: once again thisproblem is overcome by the creation of an absorbing derivative of the initialspecies following the same principle (Figure 9.22, curves c and d).

In colorimetry, it is preferable that the measurement is made on a chromophorewhose absorbance is situated toward longer wavelengths as this reduces the risk ofsuperimposition of the individual absorptions of the different other compounds.Elsewhere, when measurement is preceded by a chemical reaction, the exact struc-ture of the coloured derivative, whose absorbance is measured, is rarely known:nevertheless, if it is assumed that the reaction implicated is stoichiometric, itsmolar absorption coefficient is accessible from the molar concentration of thecompound that has been derivatized.

Abs

orba

nce

Abs

orba

nce

Wavelength (nm) Wavelength (nm)

Compound + Specific reagent Derivative

300 300400 400500 500600 600

c

d

a

b

Chromophoreincorporatedin a specificsubstance

Figure 9.22 Illustration of two situations frequently met. A compound whose absorption ismasked by the components of the mixture can otherwise be measured using colorimetry byemploying a chemical modification which transforms the molecule into a derivative sufferingno interference.


� Nephelometry, a further technique of colorimetry is also related to the Lambert–Beer law. This method consists of forming a precipitate and from the light absorbedat a given wavelength, to determine the concentration of the precursor. For example,to measure a sulphate ion, a soluble barium salt is added. A sulfate precipitate ofbarium is formed of which the absorbance is measured following stabilization with ahydrosoluble polymer such as Tween®.

9.11 Analysis of a single analyte and purity control

In practice, the first step is the construction of a calibration curve A = f �c� fromsolutions of known concentration of the compound to be measured, submitted tothe same treatment as the sample. This curve, which is most often a straight linefor dilute solutions, allows determination of the concentration Cx of the unknownsample.

Sometimes only a single standard solution is prepared. The concentration ischosen such that the concentration CR is such that its absorbance AR is slightlygreater than that estimated for the unknown solution Ax (Figure 9.23).

The following formula can then be applied to calculate Cx:

Cx = CR

Ax

AR

(9.13)

Calculation of the concentration of an analyte by expression 9.13 leads toan erroneous result if the sample contains an impurity (absent in the referencesolution) which also absorbs at the wavelength of measurement. Therefore amethod commonly named confirmatory analysis is used.

For a given pure compound the ratio of the absorption coefficients determinedat two wavelengths is constant and a characteristic of this compound (Figure 9.24).

Absorbance

Conc.

AX

AR

CR

CX

0

Figure 9.23 Calibration curve and cells of optical glass or silica glass (quartz). If a singlereference solution is prepared, the graph will be a straight line that passes through the origin.The accuracy of the result will be precise when the unknown concentration is close to thereference concentration (the result is determined by interpolation, not be extrapolation).

9.12 MULTICOMPONENT ANALYSIS (MCA) 193

Abs

orba

nce

1 - Elution of a pure compound2 - Elution of a mixture of compounds

X

Time

1 2

Abs

(m

UA

)

λ λ (nm)λ + 10

Aλ

Aλ + 10

Aλ/Aλ + 10(a) (b)

Figure 9.24 Confirmation analysis. (a) UV spectrum of a pure compound; (b) diagram illus-trating a chromatogram which presents two peaks of which the first is due to a single compoundand the second to the elution of two compounds slightly displaced in time. The evolution of theratio of absorbances during elution permits a control of the purity of the eluted compounds.These variations are usually revealed by software as coloured areas.

Thus, if one or two extra measurements are performed, displaced by severalnanometres with respect to the original measurement, the ratios of absorbanceof the sample solution can be calculated and compared with those which havebeen established in the same way using a pure reference solution. If these ratiosare different, it will be presumed that an impurity is present in the sample. Thecalculation of the concentration would not be reliable in this case.

Starting from this assumption, it is possible to control the homogeneity ofthe elution peaks in liquid chromatography on the condition that a UV detectorundertaking simultaneous measurements of the absorbance at several wavelengthsis present (such a diode array detector). Any variation during the course of theelution of a component from the ratio of the absorbances at two wavelengths,suggests that it is a mixture that is eluting from the column instead if a purecompound (Figure 9.24). This method will fail however in the case of the perfectco-elution of two compounds (the retention times being identical).

9.12 Multicomponent analysis (MCA)

When a mixture of compounds whose absorption spectra are known is analysed,then the mixture’s composition can be determined. The method is based onabsorption spectra of pure individual components and calibrating mixtures of well-defined fraction components. According to the law of additivity (expression 9.11),the spectrum of the mixture to be measured corresponds to the weighted sumof the spectra of each of the individual constituents. The classical method ofcalculation is reviewed here for revision purposes since it is no longer effectedlong hand because it is incorporated into computer software.


9.12.1 Basic algebraic method

Given a mixture of three components a, b and c in solution (concentra-tions Ca Cb Cc). The absorbances of this mixture are measured at three wave-lengths �1 �2 and �3 giving A1 A2 and A3. Knowing the values of the specificabsorbances for each of the three compounds taken in isolation for the threewavelengths (nine values in total from �1

a to �3c) through application of the addi-

tivity law, the following system of three simultaneous equations can be written (itis assumed that the optical path of the cells used is of 1 cm):

at �1 A1 = �1aCa + �1

bCb + �1cCc

at �2 A2 = �2aCa + �2

bCb + �2cCc

at �3 A3 = �3aCa + �3

bCb + �3cCc

The resolution of this mathematical system, which corresponds to a 3×3� matrix,leads to the three concentrations required Ca Cb, and Cc.

⎡⎣C1

C2

C3

⎤⎦=

⎡⎣A1

A2

A3

⎤⎦ ·

⎡⎣�1

a�1b�

1c

�2a�

2b�

2c

�3a�

3b�

3c

⎤⎦

−1

(9.14)

This approach yields good results when the compounds lead to spectra, whichare significantly different, otherwise it loses precision when the spectra are inclose proximity as a small measurement error can lead to a large variation in theresult. To avoid this risk the instruments housing diode arrays use many tensof data points. Although the system to be resolved (expression 9.14) becomesover-determined but this leads to better results.

9.12.2 Multiwavelength linear regression analysis (MLRA)

The analysis of mixtures has given rise to the development of a variety of methods,made possible with spectrometers that can record data. A computer dedicated tothe spectrometer optical platform includes quantitative analysis software that cantreat a large number of data points extracted from sample spectra under studyand for standard solutions.

Described below is a method of linear regression which leads to the neutrali-zation of the background noise and therefore to an improvement in the results.This method is applied for the analysis of a two-component sample (Figure 9.25).

The instrument uses three recordings: a spectrum of the sample (which containsthe two compounds whose concentrations are presently unknown) and a spectrumof the same spectral region for each of the pure compound (reference solutionsof known concentration).

9.12 MULTICOMPONENT ANALYSIS (MCA) 195

Wavelength(nm)

3

2

1

250 650300

0,2

0,4

0,6

0,8

400 500 600

wavelength390430450470

A, 63 ppm0.900.880.690.48

B, 96.4 ppm0.330.500.530.51

Sample0.650.740.670.55

1 - Permanganate 1*10–4 mol/L

2 - Bichromate 1*10–4 mol/L

3 - Mixture of permanganate and bichromate

Wavelength (nm)400 500 600

Abs

orba

nce

0

1A

B

Sample

Sample concentrations: A, 31.5 ppm and B, 58 ppm.

Absorbance

Absorbance

Best fit line: y = 0.5x + 0.6

Figure 9.25 Multicomponent analysis. Spectra of a solution 1 × 10−4 M of potassium perman-ganate, a solution 1 × 10−4 M of potassium dichromate and a solution containing 08 × 10−4 Mof dichromate and 08 × 10−4 M of permanganate (Bianco M. et al. J Chem Educ 1989, 66(2),178). Below is an example of MLRA from experimental data.

For any wavelength, the absorbance of the mixture of the two species a and b(which do not interact with each other) being analysed, is given by the expression(absorbance additivities):

A = �alCa + �blCb (9.15)

For each of the two reference spectra, supposing that the thickness of the measuringcell is l = 1 cm, the following equations can be written :

For compound a Aref a = �a · Cref a (9.16)

For compound b Aref b = �b · Cref b (9.17)

These two expressions lead to the calculation of the molar absorption coefficients �of each pure constituent, at each wavelength considered. Therefore expression 9.15can be re-written as:


A = Aref a

Cref a

Ca + Aref b

Cref b

Cb (9.18)

By dividing the first element by Aref a, then for each wavelength:

(A

Aref a

)= Ca

Cref a

+ Cb

Cref b

·(

Aref b

Aref a

)(9.19)

The first member of relation 9.19 is therefore an affinity function of the ratio ofabsorbances figuring in the second member. The calculated values are on a straightline whose slope and intercept enable calculations to be made for Ca and Cb.

The precision of the results increases with the number of data points used. Themethod needs a computerized spectrophotometer.

9.12.3 Deconvolution

Numerous software data treatments authorize the elucidation of mixture compo-sition from spectra. One of the best-known methods is the Kalman’s least squaresfilter algorithm, which operates through successive approximations based uponcalculations using weighted coefficients (additivity law of absorbances) of theindividual spectra of each components contained in the spectral library. Othersoftware for determining the concentration of two or more components withina mixture uses vector quantification mathematics. These are automated methodsbetter known by their initials: PLS (partial least square), PCR (principal componentregression), or MLS (multiple least squares) (Figure 9.26).

9.13 Methods of baseline correction

Some samples, such as biological fluids, contain micelles or particles in suspension,which by light scattering (Tyndall effect) induce a supplementary absorption. Thisone varies in a regular manner with the wavelength (Figure 9.27).

There are several methods that seek to correct this phenomenon by extractingfrom the absorbance measured what is not due to the analyte. These are infact corrections made to the baseline from measurements undertaken at differentwavelengths.

9.13.1 Modelling by polynomial function fitting

Supposing that variations in the baseline could be represented by a functionA = k�n. To find k and n, a region of the spectrum is located in which the analyte

9.13 METHODS OF BASELINE CORRECTION 197

Abs

orba

nce

Wavelength

Figure 9.26 Deconvolution of a spectral curve. From the experimental spectrum of a mixtureof five compounds (the external trace on the figure), the software is able to find the proportionof each one (it is assumed that the individual spectra of the individual components are known).

Abs

orba

nce

Abs

orba

nce

λ1λ1 λ2λ2 λ3λ3

A′

A′2A1

A2

A3

x

y

nm

nm

a

b

(a) (b)

Figure 9.27 Illustration of the concepts behind Morton and Stubbs’ calculation.

does not absorb in order that the software might use this zone to calculate thesecoefficients by the method of least squares (knowing that log a = log k + n log �).By consequence, whatever the wavelength of measurement it will be possible toremove the absorbance corresponding to the baseline.

9.13.2 Morton–Stubbs three-point correction

The method of Morton and Stubbs (as well as the method using derivative curves(cf. Section 9.15), leads to an efficient correction of the baseline on conditionthat the underlying absorption varies linearly in the zone of measurement. Ina situation such as that represented by Figure 9.27a, in order to quantify the


compound, the absorbance A2 read at the maximum �2 must be corrected byremoving the absorbance corresponding to the values noted as x and y.

To bring this about, a reference spectrum of the pure compound must be madein order to choose two wavelengths �1 and �3 whose absorbance coefficients arethe same (Figure 9.27b). As on the figure at, �1 and �3 this compound has thesame absorbance A′ and an absorbance maxima A′

2 at the wavelength �2. Theratio R between these two values is calculated �R = A′

2/A′�. Next on the samplespectrum, the ratio of the absorbances is calculated at these same two wavelengths.On the condition that the baseline is a line of the same slope as the segment ab,the value of x can then be calculated (see figure):

x = �A1 − A3��3 − �2�

��3 − �1�(9.20)

From R and the ratio A2/A3 of the sample, y can be deduced, knowing thatthe ratio of the absorbances, after the correction of x and y, has the value R(Figure 9.26):

R = A2 − �x + y�

A3 − y

thus,

y = RA3 − A2 + x

R − 1(9.21)

Substracting x and y from A2 leads to the calculation of the corrected absorbance,according to

A = A2 − x − y

This last equation, which is independent of the concentration of the referencesolution yields satisfactory results. This method requires only to have at one’sdisposal a spectrum of the pure compound.

9.14 Relative error distribution due to instruments

For many contemporary spectrophotometers it is possible to measure absorbanceup to within 4 or 5 units. These high values correspond to transmitted intensitiesthat are extremely weak (I/I0 = 10−5 for A = 5), giving results that are consideredas less reliable.

For transmittance measurements three types of error are recognized as beingdue to the instrument. These are of independent origin and are potentially accu-mulative (Figure 9.28):

• The background noise of the light source. Represented by the term �T1 isconsidered to be constant and independent of T � �T1 = k (curve 1).

9.14 RELATIVE ERROR DISTRIBUTION DUE TO INSTRUMENTS 199

0

0.02

0.04

0.06

0.08

0.1

0 20.5 1.5

Absorbance

1

4

23

ΔC/C

Rel

. Std

. Dev

. on

C

1

Figure 9.28 Relative errors in quantitative UV spectrometry. Curves representing the averageof each of these errors (1 to 3) in absorbance measurements, as well as the relative standarddeviation (RSD) of concentration determination as a function of absorbance resulting fromtheir sum (4).

• The background noise of the photomultiplier tube (or photodiode). Representedby the term �T2 varies as a function of T following a complex relationshipand is represented by the following equation (curve 2):

�T2 = k2

√T 2 + T (9.22)

• Stray light. Corresponds to the light which does not pass through the samplebut reaches the detector. It decreases the apparent concentration in the samplecell. This term is proportional to T � �T3 = k3T (curve 3).

As these sources of error are additive, the total error in the concentrationcorresponds – in accepting the three expressions above – to a curve whose ordinateof each point is the sum of the ordinate of the three individual errors discussedabove. This curve passes through a minimum generally located around A = 07.For quantitative measurements it is therefore advisable to adjust the dilutions inorder that the absorbances are situated in this favourable domain.

From the Lambert–Beer law it is also possible to link relative standard deviation(see Section 22.2) on the measurement of concentration C to the relative standarddeviation made on the transmittance T (curve 4).

�C

C= 1

ln T· �T

T(9.23)


9.15 Derivative spectrometry

The principle of derivative spectrometry consists of calculating, by a mathemat-ical procedure, derivative graphs of the spectra to improve the precision of certainmeasurements. This procedure is applied when the analyte spectrum does not appearclearly within the spectrum representing the whole mixture in which it is present.This can result when compounds with very similar spectra are mixed together.

The traces of the successive derived spectral curves are much more uneven thanthe one of the original spectrum (called zeroth order spectrum). These derivativeplots amplify the weak slope variations of the absorbance curve (Figure 9.29).The procedure of obtaining the first derivative graph, dA/d�= �d�/d��lC, can beextended to successive derivatives (nth derivatives).

The curve of the second derivative matches the points of inflection in the zerothorder spectrum by regions of zero slope which correspond to maxima or minima(Figure 9.30). The fourth derivative reveals even further the weak absorbancevariations in the initial spectrum. Numerous analyses would be improved byadopting this principle, knowing that to make a measurement from the derivativespectra is no more difficult than from the absorbance spectrum. The amplitudebetween the maxima and the minima of the nth derivative graph is proportionalto the absorbance value of the solution. The calibration graph is established from afew standard solutions of different concentrations to which the same mathematicaltreatment has been applied, as to the sample solution.

Interest in this procedure manifests itself in three situations in which theabsorbance is altered:

d2A /dλ2

Wavelength

240 300260 280

Absorbance

Arb

. Uni

ts

C6H5CH2CH(NH2)CO2H

nm

Figure 9.29 Derivative curve. UV spectra of phenylanaline and the curve of its secondderivative.

9.15 DERIVATIVE SPECTROMETRY 201

0

0.2

0.4

0.6

0.8

1

200 250 300 350 400 450 500Wavelength (nm)

Wavelength (nm)

Abs

orba

nce

−0.2

−0.1

0

0.1

0.2

200 250 300 350 400 450 500

Firs

t der

ivat

ive

(arb

. uni

ts)

10%

1%

A

A ′

B

B ′

dA/Dλ

Figure 9.30 Effect of light scattering on the absorbance spectrum and on its first derivative curve.Comparison of the derivative graphs corresponding to A the spectrum of a compound insolution without light scattering and to B, the same spectrum, in the presence of scattering.The phenomenon can be seen to disrupt up to 10 per cent of the absorbance on the regulargraph yet only around 1 per cent of the value of the amplitude of the derivative curve (spectramodelled from functions corresponding to Gaussian curves).

• If the spectrum of the sample in solution suffers from an increasingabsorbance towards higher energy by consequence of a uniform baselineabsorption, the derivative curve, which is sensitive only to variations of slopeof the zeroth order curve, will not be affected.

• If light scattering occurs in the heart of the sample solution (which producesan absorption baseline growing moderately at shorter wavelengths), again,the derived graphs will be little affected (Figure 9.30).


• If the absorbance due to the analyte, almost invisible on the original spectrum,is overshadowed by the main absorbance arising from the matrix.

9.16 Visual colorimetry by transmission or reflection

Visual colorimetry, used for more than four centuries, is a simplified form ofinstrumental absorption spectrometry. Given its modest cost and its frequentlysurprising precision it is therefore widely practised.

The simplest colorimeters, used for routine measurements, were visual compara-tors (Figure 9.31). Nessler tubes, used for many years, consisted of graduatedflat-bottomed tubes of glass filled with different concentrations of standard solu-tions mixed with a derivatising agent. The solution to be analysed was placed withthe same agent in an identical tube and colour was compared with that of thestandards (‘same colour, same concentration’).

For this purpose, these tubes were placed over a source of white light, to beobserved in transmission. These selective tests, ready to use and requiring noinstrumentation, complement established methods and by their rapidity help toextend the range of semi-quantitative analyses.

� The innumerable tests, presented in the form of strips, which colour more orless intensely when soaked in the appropriate medium, are among many currentapplications of colorimetry. However, a result, derived from a visual examination of thereflected light should rather be associated with reflectometry rather than transmissioncolorimetry.

Blank Sample treated

1

23

4

5 6

Figure 9.31 Visual colorimetry. Left, a disc comparator. The use of this apparatus consists ofchoosing, by rotation of the filter holder, the filter which permits when it is superimposed uponthe analytical blank, a match of the colour of the tube. The observation is made by transmissionof white light. The central tube contains the sample after treatment. The disc is calibratedfor a particular measurement. Right, a portable colorimeter which allows comparisons withoutevaluation by the human eye (Model 1200, reproduced courtesy of LaMotte Company).

PROBLEMS 203

Problems

9.1 Calculate the energy of a mole of photons corresponding to a wavelength of300 nm.

9.2 Calculate the absorbance of an organic dye �C =7× 10−4 mol L−1�, knowingthat the molar absorptivity � = 650mol L−1 cm−1 and that the length ofthe optical path of the cell used is 2 × 10−2 m. What would happen to theabsorbance if the cell used was of double its present thickness?

9.3 A 128 × 10−4 M solution of potassium permanganate has a transmittance of0.5 when measured in a 1 cm cell at 525 nm.

1. Calculate the molar absorptivity coefficient for the permanganate at thiswavelength.

2. If the concentration is doubled what would be the absorbance and thepercentage transmittance of the new solution?

9.4 A polluted water sample contains approximately 0.1 ppm of chromium,�M = 52g mol−1�. The determination for Cr(VI) based upon absorption byits diphenylcarbazide complex ��max = 540nm �max = 41700Lmol−1 cm−1�

was selected for measuring the presence of the metal. What optimum path-length of cell would be required for a recorded absorbance of the orderof 0.4?

9.5 Paints and varnishes for use on exteriors of buildings must be protectedfrom the effects of solar radiation which accelerate their degradation (photol-ysis and photochemical reactions). Given that: M = 500g mol−1; �max =15000Lmol−1 cm−1 for �max = 350nm, what must be the concentration(expressed in gL−1) of a UV additive M such that 90% of the radiation isabsorbed by a coating of thickness 0.3 mm?

9.6 By employing the empirical rules of Woodward–Fieser, predict the positionof the maximum absorption of the compounds whose structures are seenbelow.


9.7 To determine the concentrations (mol/L) of Co�NO3�2 (A) and Cr�NO3�3

(B) in an unknown sample, the following representative absorbance data wereobtained.

A (mol/L) B (mol/L) 510 nm 575 nm

15 × 10−1 0 0714 00970 6 × 10−2 0298 0757Unknown Unknown 0671 0330

Measurements were made in 1.0 cm glass cells.

1. Calculate the four molar absorptivities: �A�510�, �A�575�, �B�510� and �B�575�.

2. Calculate the molarities of the two salts A and B in the unknown.

9.8 The determination of phosphate concentration in a washing powder requiresfirst the hydrolysis of the tripolyphosphate components into the phos-phate ion or its protonated forms. Then a quantitative colorimetric methodbased upon the absorption of the yellow complex of phosphate and ammo-nium vanadomolybdate can be used. A series of standard solutions wasprepared. The complex was then developed in 10 mL aliquots of thesesolutions by adding a 5.0 mL aliquot of an ammonium vanadomolybdatesolution.

Measurements were made in a glass cell of 1.0 cm pathlength at 415 nm.The following absorbance data were obtained.

1. Produce a calibration curve from these data.

2. By the method of least squares, derive an equation relating absorbanceto phosphate concentration.

PROBLEMS 205

Solutions Concentration (mmol/L) Absorbance

S0 00 0S1 01 015S2 02 028S3 03 04S4 04 055S5 05 07

3. An unknown solution obtained by hydrolysis of 1 g of detergent treatedin an identical way gave an absorbance of 0.45. Determine the phosphateconcentration of this solution.

9.9 The concentration of the sulphate ion in a mineral water can be determinedby the turbidity which results from the addition of excess BaCl2, to a quantityof measured sample. A turbidometer used for this analysis has been stan-dardised with a series of standard solutions of NaSO4. The following resultswere obtained:

Standard solution Conc. SO2−4 �mg/L� Reading of

turbidometer

S0 000 006S1 500 148S2 1000 228S3 1500 398S4 2000 461

1. In supposing that a linear relationship exists between the readings takenfrom the apparatus and the sulphur ion concentration, derive an equa-tion relating readings of the turbidometer and sulphate concentration(method of least squares).

2. Calculate the concentration of sulphate in a sample of mineral waterfor which the turbidometer gives a reading of 3.67.

10Infrared spectroscopy

Analytical infrared studies are based on the absorption (or reflection) of theelectromagnetic radiation that lies between 1 and 1000�m. This is one of themost common spectroscopic techniques used for compound identification andmeasuring of concentrations in many samples. This spectral range is sub-dividedinto three smaller areas, the near infrared (near-IR, 1–2�5�m), the mid infrared(mid-IR, 2�5–50�m) and the far infrared (beyond 25�m). Although the near-IRis poor in specific absorptions, it is considered as an important method by qualitycontrol laboratories for quantitative applications. By contrast the mid-IR regionprovides more information upon the structures of compounds and consequentlyit is much used as a procedure for identifying organic compounds for which itremains a form of functional group fingerprinting. The far IR requires the useof specialized optical materials and sources. To conduct these analyses there is afull range of instruments from Fourier transform spectrometers to a multiplicityof analysers of dispersive or non-dispersive types, specialized in the measurementof pre-defined compounds (e.g. analysis of gases and vapours) or which allowcontinuous analyses on production lines. The Fourier transform infrared spec-trometry offers numerous possibilities for the treatment of spectra and has appli-cations for the analysis of structured microsamples (infrared microanalysis).

10.1 The origin of light absorption in the infrared

In the near and the mid infrared, the absorption of light by matter originatesfrom the interaction between the radiation from a light source and the chemicalbonds of the sample. More precisely, if the atoms situated at the two extremesof a bond are different, they form an electric dipole that oscillates with a specificfrequency. If such a non-symmetrical bond is irradiated by a monochromaticlight source whose frequency is the same as the dipole, then an interaction willoccur with the bond. Thus, the electrical component of the wave can transfer itsenergy to the bond on condition that the mechanical frequency of the bond andthe electromagnetic frequency of the radiation are the same (Figure 10.1). Thissimplified approach can be used to rationalize that in the absence of a permanent


208 CHAPTER 10 – INFRARED SPECTROSCOPY

(a)

Mechanical oscillations Mechanical oscillations

Time

Time

Time

Light waved

d

(b)

dd

ν

Figure 10.1 Mechanical interpretation of the interaction between a light wave and a polar bond.The mechanical frequency of the wave is not altered by the absorption of a photon, only itsamplitude of oscillation increases.

dipole, which is the case with O2�N2 and Cl2 having non-polar bonds, there willbe no coupling with the electromagnetic wave and therefore no absorption ofenergy will take place. In the mid-IR these bonds are labelled ‘transparent’.

10.2 Absorptions in the infrared

Infrared absorption information, which varies with the radiation wavelengthsselected, is generally presented in the form of a spectrum, which is the basicdocument issued from the spectrometer. The ordinate of the graph records theratio of the transmitted intensities, that is with and without sample, calculated foreach wavelength marked on the abscissa. This ratio is called the transmittance (T ).On the graph it is often replaced by the percent transmittance (per cent T ) or byabsorbance (A), the logarithm to the base 10 of the reciprocal of the transmittance:A = log�1/T �. If the study has been conducted using reflected or diffused lightthen units of pseudo-absorbance will have been used (cf. Section 10.9.2). Finally, ithas become appropriate to substitute the values of wavelengths by their equivalentexpressed in wavenumbers � whose units are in cm−1 or kaysers, (formula 10.1).Figure 10.2 corresponds to a spectrum recorded in the mid-IR, between 2.5 and25�m.

�cm−1 = 1

�cm

(10.1)

10.3 Rotational–vibrational bands in the mid-IR

Excepting when the temperature is 0 K, atoms within molecules are in perpetualmotion and each one of them possesses three degrees of freedom, which referto the three classic Cartesian coordinates. All of these movements confer uponeach isolated molecule a combined mechanical energy. The theory is postulated

10.3 ROTATIONAL–VIBRATIONAL BANDS IN THE MID-IR 209

Wavenumber (cm–1)

Polystyrene film (35µm)Mon May19 15:59:24 - 2003Number of scans, sample:5Number of scans, background:5Resolution :4cm-1Gain:2

4000 3500 3000 2500 2000 1500 1000

90

80

70

60

50

40

30

20

10

0

% T

rans

mitt

ance

Figure 10.2 Mid-IR spectrum of a polystyrene film. The typical representation of an infraredspectrum with a linear scale abscissa in cm−1 (see formula 10.1) for an easier observation of theright-hand section and with percentage transmittance along the ordinate. The transmittance issometimes replaced by the absorbance A�A=− log T�. The scale, in cm−1, (or kaysers) is linearin energy �E = hc/�� and will decrease from left to right (i.e. from high to low energy).

that the total molecular energy arises from the sum of the independent thoughquantified terms named energy of rotation Erot, energy of vibration Evib andelectronic molecular energy Eelec:

Etot = Erot + Evib + Eelec (10.2)

The values of these energies are very different and according to the Born–Oppenheimer principle they can vary independently of each other.

In the mid-IR, a source emitting a radiation of 1000 cm−1 corresponds to aphoton energy E = hc� = 0�125 eV. If such a photon is absorbed by a moleculeits total energy will be increased by this energy. Theoretically the term Evib willbe modified but the term Eelec will not change because this energy is too weak tocause transition between two different electronic levels.

In practice, as samples are usually in the form of condensed (liquid) or solidphases, pure or in solution and not in the form of isolated species, numerousdipole-dipole interactions are produced between the species present, which perturbboth the energy levels and the absorption wavelengths. Thus a spectrum is alwaysin the form of broadened signals called bands which extend over tens of cm−1,which common apparatus are unable to separate into individual transitions.

It is noteworthy that the width of an absorption signal is inversely proportionalto the lifetime of the excited state (Heisenberg’s uncertainty principle). Hence, forgases, the lifetime is long and the absorption lines are sharp. This is why smalldi- or triatomic molecules sampled in the gas state and at low pressures can leadto spectra containing narrow regular bands whose positions enable the elucidationof the various energetic states predicted by the theory.


R equilibrated

R maximum

R minimum

x0x0

Figure 10.3 A diatomic molecule represented in the form of an harmonic oscillator. The termharmonic oscillator comes from the idea that the elongation is proportional to the force exerted,from which the frequency �vib is independent.

10.4 Simplified model for vibrational interactions

For modelling the vibrations of bonds, a harmonic oscillator should be imagined,which comprises two masses linked by a spring and able to slide in a plane withoutfriction (Figure 10.3). If the two masses are displaced by a value x0 with respectto the equilibrium distance Re and then the system is released, it will begin tooscillate with a period that is a function of the constant relating to the stiffness ofthe spring, named force constant k (N/m) and of the size of the masses involved.

The frequency, which is independent of the elongation, is given by Hooke’s law(expression 10.3) in which � (kg) represents, as indicated, the reduced mass ofthe system.

�vib = 1

2

√k

�(10.3)

with

� = m1m2

m1 + m2

(10.4)

The vibrational energy of this simple model can vary in a continuous fashion.Following a short elongation x0 with respect to the distance from equilibriumRe�Evib becomes:

Evib = 1

2kx2

0 (10.5)

For a bond

� = 1

2c

√k

�(10.6)

10.4 SIMPLIFIED MODEL FOR VIBRATIONAL INTERACTIONS 211

with

� = 1

�= �

c(10.7)

The model above can be approximated to the chemical bond linking two atoms,on condition that the quantum theory governing species of atomic dimensionsis employed. Because a bond whose frequency of vibration is � can absorb lightradiation of an identical frequency, its energy will increase from the quantumE=h�. According to this theory, the simplified expression 10.8 will yield possiblevalues for Evib:

Evib = h��V + 1/2� (10.8)

V = 0�1�2 � � � is called the vibrational quantum number of vibration andcan only vary by one unit (V = +1, the ‘single quantum transition’). Thedifferent values of expression 10.5 are separated by the same interval Evib = h�(Figure 10.4).

At room temperature, the molecules are still in the non-excited state V =0, thatis, E�vib�0 = 1/2h� (energy at 0 K). Besides the standard transition V = +1, thatcorresponding to V = +2 and ‘forbidden’ by this theory, appears weakly whenthe fundamental absorption band is particularly strong (for example, in the caseof elongation vibrations in organic compounds containing a carbonyl bond C=O(e.g. ketones or aldehydes).

� No mode of valence vibration is situated higher than 3960 cm−1 (H-F). This is thewavenumber which determines the frontier between the mid and the near infrared.However, for reasons of usefulness, many current spectrometers accommodate bothnear and mid-IR permitting a coverage from 400 up to 8000 cm−1.

V = 1

V = 0

V = 2

E = 1/2 hν

E = 3/2 hν

E = 5/2 hν

E0

E1

E2E2

E1

E0

E

(a) (b)

Figure 10.4 Diagram of the vibrational energies levels of a bond. (a) For isolated molecules;(b) for molecules in the condensed phase. The transition V = 0 to V = 2 corresponds to a weakharmonic band. Bearing in mind the energies of photons in the mid-IR it can be calculated thatthe first excited state �V = 1� is 106 less occupied than the ground (fundamental) state. Theharmonic transitions are exploited in the near-IR.


10.5 Real compounds

The harmonic oscillator model does not take into account the real nature ofchemical bonds, which are far from being perfect springs. The force constantk diminishes if the distance between the atoms is stretched, yet in contrast,increases strongly if the atoms are pushed close together. More precise modelsemploy correction terms related to the anharmonicity of experimentally observedoscillations.

Elsewhere, in the mid-IR, photon energy is sufficient to modify the quantizedterms Evib and Erot in expression 10.2. This is therefore a vibration–rotationspectrum, that is, several tens of rotational transitions accompany each vibrationaltransition. For the simplest molecules it is possible to interpret particular aspects ofthe absorption bands. Experience and theory have enabled rules of the permittedtransitions to be drawn up. Small molecules as carbon monoxide and hydrogenchloride (Figure 10.5) have been intensely studied from this point of view.

Knowing that Eelec doesn’t vary in the mid-IR, expression 10.2 leads to theenergy values corresponding to the bands of absorption (Figure 10.5):

EVR = �EVR�2 − �EVR�1 = Evib + Erot (10.9)

Each atom has three degrees of freedom, corresponding to motions along anyof the three Cartesian coordinate axes �x� y� z�. Thus a polyatomic molecule of ninteracting atoms can be defined by 3n degrees of freedom (see Section 10.3). Sinceit requires 3 coordinates to define its centre of gravity (translational movementof the molecule), the remaining 3n − 3 are internal degrees of freedom corre-sponding to vibrations. In general 3 are required to define the rotation of the entiremolecule. All of the others correspond to the fundamental vibrations (i.e. 3n− 6).A molecule containing 30 atoms will have 84 normal modes of vibration, happilynot all active, since there must first be variation in the dipole moment to get anabsorption. Such a high number of energy levels, to which are added combinationsof levels and harmonics, can only lead to complex and unique spectra for eachcompound.

10.6 Characteristic bands for organic compounds

The application of the above rules to all kinds of compounds has been made inorder to exploit the use of infrared spectroscopy as a method of structural analysis.Empirically, it has been observed a correlation between position of certain bandmaxima and the presence within a molecule of organic functional groups or ofparticular structural features within the skeleton of molecules (see Table 10.1).This property comes from the fact that each organic functional group corres-ponds to a collective-type of several atoms. For a given bond, the force constantk (expression 10.3) does not vary significantly from one molecule to another.

10.6 CHARACTERISTIC BANDS FOR ORGANIC COMPOUNDS 213

R(3) R(2) R(1) R(0) (Q) P(1) P(2) P(3) P(4)

012

3

V = 1

012

3 V = 0

J

J

4

4

n

R branch P branch(Q)

E

Abs.

Tra

nsm

ittan

ce

2200 2100 2050 cm–1

(a)

(b)

(c) Carbon monoxide spectrum

Wavenumbers

2150

Figure 10.5 Rotation/vibration levels of carbon monoxide. V and J are the quantum numbersof vibration and rotation. The fundamental vibration corresponds to V = +1 and J = +1. (a)A rotation-vibration band corresponds to all of the allowed quantum transitions. If the scaleof the diagram is in cm−1, the arrows correspond to the wavenumbers of the absorptions; (b)branch R corresponds to J = +1 and the band P to J = −1. They are situated either sideof band Q, absent from the spectrum (here it can be supposed that J = 0 correspondingto a forbidden transition); (c) below, vibration–rotation absorption band of carbon monoxide(pressure of 1000 Pa). The various lines illustrate the principle of the selection rules. The differ-ence (wavenumbers) between successive rotational peaks are not constant due to anharmonicityfactors.

Tabl

e10

.1C

orre

lati

onC

har

tin

the

mid

-Infr

ared

betw

een

funct

ional

grou

psan

dab

sorp

tion

bands

2000

1900

1800

1700

Alk

anes

Alk

enes

Am

ines

Ket

ones

Est

ers

Am

ides

Alk

ynes

Aro

mat

ics

Alc

ohol

s/P

heno

ls

Eth

ers

Ald

ehyd

es

Car

boxy

lic A

cids

Nitr

o C

ompo

unds

4000

3500

3000

2500

1600

1500

1400

1300

1200

1100

1000

900

800

700

N–H

N–H

–N

Hñ–

NH

N–H

O–H

O–H

(Dim

er )

O–H

O–H

O–H

C–N

C–N

C–O

C–O

C–O

C–O

– –C

C

– –C

C

– –O

C – –O

C – –O

C

– –O

C

– –O

C

–C–H

C–H

C–H

– ––

CH

– –––

CH

– ––C

C

– ––

CH

O

Alk

yl.

Alk

yl. A

ryl.

Ary

l.

1 or

2 B

ands

Prim

.P

rim.

Prim

.

Sat

.

Sat

.

Sat

. Sat

.

Uns

at.

Uns

at.

Uns

at.

Uns

at.

Cyc

l.

Sec

.S

ec.

Sec

.

Ph.

Tert

.P

rim.

Sec

.

1′1′

2′

3′

4′5′

ab

cd

e

–NO

2 2

Ban

ds

CH

2 an

d C

H3

Str

etch

ing

Vib

ratio

ns (

ν)In

the

plan

e B

endi

ng V

ibra

tions

( δ)

Out

-of-

plan

e B

endi

ng V

ibra

tions

(γ)

Abb

revi

atio

nsS

at.,

Sat

urat

edU

nsat

., U

nsat

urat

ed

Prim

., P

rimar

yS

ec.,

Sec

onda

ryTe

rt.,

Tert

iary

a 1

H I

sola

ted

b 2

H A

djac

ents

c 3

H A

djac

ents

d 4

H A

djac

ents

e 5

H A

djac

ents

1′ -

CH

=C

H2

2′ -

CH

=C

H-

(tr

ans)

3 ′ -

C=

CH

2

4′ -

C=

CH

-5 ′

-C

H=

CH

- (

cis)

(CH

2)n>

4

(cm

–1)

(Dim

er )

Prim

.S

ec.

– ––

CH

C

10.6 CHARACTERISTIC BANDS FOR ORGANIC COMPOUNDS 215

γ CHγ CHδ CH

Stretching vibration (sym.) Stretching vibration (asym.) Planar rotation (rocking)δ CH (Bending)

C

H

Scissoring(Bending)

Wagging (out of plane)(Bending)

Twisting (out of plane)(Bending)

Figure 10.6 Major vibrational modes for a non-linear group: the CH2. Characteristic stretchingand bending vibrations in and out of the plane. In IR spectroscopy, the position and the intensityof the bands are modified by associations between molecules, solvent polarity, etc.

Moreover, calculation reveals that the reduced mass of a given group of atomstends toward a limiting value as the molecular mass increases (see expression 10.4).This can explain that absorption of each organic functional group corresponds toa particular value.

The most widely known molecular movements are stretching vibrations(symmetrical and asymmetrical) and bending vibrations of angular deformation(Figure 10.6). Alternately, in the region of the spectrum below 1500 cm−1, theabsorption bands are numerous and differ for each compound. These are defor-mation vibrations of both the bonds and the skeleton and are difficult to assignwith accuracy.

For instrumental reasons, the spectral range, which extends from 1 to 2�5�m(though it has no formal limits) has for a long time been ignored. However thetandem progress of both detectors and transparent fibre optics in the near-IRlinked with advances in chemometric methods has permitted the developmentof the region. The spectra are often presented as curves without clearly definedpeaks. Nevertheless, each recording is representative of the sample and thereforecan be used as a fingerprint. For organic compounds, the absorption bands inthe near-IR originate from either harmonic bands or a combination of the funda-mental vibrations of the C–H, O–H and N–H bonds (which are situated close to3000–3600 cm−1).

As for carbonyl compounds, the first two harmonics of the fundamental vibra-tion of C=O �1700 cm−1� appear towards 3400 and 5100 cm−1 respectively. Thecombination bands result from the interaction of two or more modes of vibrationfor the same functional group and are superimposed upon the preceding band.The energy of the corresponding transition is approximately the sum of thosewhich have given rise to it.


� Chloroform, which absorbs at 3020 cm−1 and 1215 cm−1 will also absorb at4220 cm−1, which approximately represents the sum of the two preceding values.

10.7 Infrared spectrometers and analysers

These instruments (Figure 10.7) can be divided into two categories: the Fourier trans-form spectrometers, which undertake a simultaneous analysis of the whole spectralregion from interferometric measurements, and numerous specialized analysers forthe second category. Dispersive-type spectrometers are also used for the near-IR.

The first category uses a Michelson-type interferometer or similar device,coupled to a specialized microprocessor for calculating the spectrum, while thesecond category uses filters or a monochromator with a motorized grating thatcan scan the range of frequencies studied (Figure 10.7).

Dispersive spectrometers. For a long time, mid-IR spectrometers were constructedon the principle of the double beam design. This fairly complex optical assembly,which remains in use for the UV/Vis, yields progressively over real time the

Source

Monochromator

Detector

Recorder

ex. T = 0.85(A = 0.07)

Sample orReference

(a) Source

Monochromator

Sector mirror

Detector

Recorder

Sample orReference

(b) Source

Interferometer

Detector

SignalProcessing

Sample

(c)

Figure 10.7 Schematic diagram of spectrometers and analysers in the infrared. (a) Single beamanalyser containing a fixed monochromator or a filter used when a measurement at a singlewavelength will suffice; (b) dispersive spectrometer, double beam system. In contrast to spec-trophotometers in the UV/Vis, the sample, located prior to the monochromator is permanentlyexposed to the full radiation of the source, knowing that the energy of the photons in this regionis insufficient to break the chemical bonds and to degrade the sample; (c) Fourier transformsingle beam model.

10.7 INFRARED SPECTROMETERS AND ANALYSERS 217

spectrum of the sample through the measurement of the transmittance, calculatedfor each wavelength by comparing the intensity of light arising from two separatepathways, one serving as reference and the other passing through the sample. Tothis end the light issuing from the source is separated by a series of mirrors intotwo beams one of which passes through the sample compartment and the otherthrough the reference chamber. The light is directed to a diffraction grating. Foreach small wavelength interval, defined by the monochromator, the light followingeach of the two pathways focuses on the detector alternatively. This arrangementis effected by an optical chopper, such a sector mirror which rotates about tentimes per second. The ratio of the signals obtained, at practically the same instant,corresponds to the transmittance for the wavelength considered. Each wavelengthis measured one at a time These dispersive instruments are sometimes calledgrating or scanning spectrometers.

10.7.1 Fourier transform infrared spectrometer (FTIR)

An FTIR spectrometer contains a single beam optical assembly with, as an essentialcomponent, an interferometer – often of the Michelson type – located betweenthe source and the sample (Figure 10.7c). It consists of three active components:a moving mirror, a fixed mirror and a beam-splitter.

The radiation issuing from the polychromatic source impacts on the beam-splitter acting as a separator, which is made of a semi-transparent film of germa-nium deposited on a KBr support. This device divides the original beam into twohalves, one of which is directed towards a fixed mirror and the other towardsa moving mirror whose distance from the beam-splitter varies. Recombined,these two beams follow the same optical path passing through the sample beforereaching the detector that measures the global light intensity received. This is amultiplexing procedure applied here to the domain of optical signals. The heartof the Michelson interferometer is a moving mirror, the sole mobile compo-nent that oscillates between two extreme positions. When its position is suchthat the pathways travelled by the two beams have the same length until thedetector (zero optical path difference), then the light composition of the beamleaving the interferometer is identical to that which enters. In contrast, when themobile mirror changes of this particular position, the light leaving has a spec-tral composition which depends upon the phase difference of the two beams:the signal transmitted over time by the detector is recorded in the form of aninterferogram:

�Total Int�� = f ��

with � representing the path difference between both beams (Figure 10.8).The management of the optical bench and the acquisition of the data is

controlled by a specific electronic interface. During the displacement of the mirror,an ADC converter, linked to the detector, samples the interferogram in the form of


S

Sample

Detector

Source

Laser

Laserdetection

Detail of a Beam splitterKBr/Germanium

Interferometer Optical path of an IRTF

d

x

IR Source

Iris

Collimating mirror

KRS-5 Window

focussing mirror

Detection of laser

Samplecompartment

Detector

Moving mirror

Sealed optic

Ne Laser

(a) (b)

fixed mirror

mobile mirror

Figure 10.8 The optical assembly of a Fourier transform apparatus. (a) 90 � Michelson interfer-ometer with below, some details of the beam-splitter; (b) the optical diagram of a single beamspectrophotometer (picture of Shimadzu model 8300). A low power He/Ne laser is used as aninternal standard (632.8 nm) in order to locate with precision the position of the mobile mirrorby an interference method (this second sinusoidal interferogram which follows the same opticalpathway, is used by the software to determine the optical path difference).

thousands of data points. Each of these values corresponds to a position and repre-sents the global intensity that passes through the sample. This is the second termof a linear equation in which the unknowns correspond to the amplitudes of the ndifferent wavelengths (assumed to be a finite number) considered for the mirrorand after absorption by the sample. From these thousands of values a specializedmicroprocessor will execute, in less time than it would take to describe, using theCooley algorithm the calculation of a giant matrix leading to the amplitude ofeach wavelength of the spectral band studied.

Bearing in mind a resolution factor imposed by the method of calculation, theclassical representation of the spectrum is obtained, I = f �� or I = f ��. Accordingto Nyquist’s theory, at least two points per period are required in order to find,by calculation, a given wavelength of the spectrum. To obtain a sample spectrumequivalent to the one obtained with a double beam spectrometer, two spectra oftransmitted intensities are recorded: the first, without sample (absorption back-ground) and the second with sample. The conventional spectrum, in percentageT , is obtained from these two spectra (Figure 10.9).

10.7 INFRARED SPECTROMETERS AND ANALYSERS 219

10

20

30

40

50

60

70

80

90

50010001500200030004000Wavenumber (cm–1)

% T

rans

mitt

ance

Spectrum after calculating ratio of emittances 2 /1

FTIR is a simultaneous method in the sensethat it treats the signal in a global manner.

Each point of the spectrum has beencalculated from all of the given data

TF

500100015002000

–5

–4

–3

–2

–1

0

1

2V

olts

Vol

ts

Interferogram

without sample

Number of scans: 4Resolution: 4 cm–1

Gain 1

points

May 19 2003

5

10

15

20

25

30

35

40

45

50

55

50010001500200030004000Wavenumber (cm–1)

Single beam spectrum I0 = f(ν)


Gain 1

Background

1

May 19 2003

500100015002000

–5

–4

–3

–2

–1

0

1

2

Interferogram

with sample


Gain 2

Sample

points

FT

May 19 2003

0

5

10

15

20

25

30

35

40

50010001500200030004000

Single beam spectrum I = f(ν)


Gain 2

Sample

2

May 19 2003S

ingl

e be

amS

ingl

e be

am

Figure 10.9 Sequence for obtaining a pseudo-double beam spectrum with a Fourier transforminfrared spectrometer. The apparatus records and memorizes two spectra, which represent thevariations of I0 (the blank) and I (sample) as a function of the wavenumber (these are emissionspectra 1 and 2). Next the conventional spectrum is calculated, identical to that of an instrumentof the double beam type, by calculating the ratio T = I/I0 = f �� for each wavenumber. Strongatmospheric absorption (CO2 and H2O), which is present along the optical path is eliminatedin this way. The illustrations correspond to the spectrum of a polystyrene film.


� The French mathematician J.-B. Fourier (1768–1830) could never have imaginedhow famous he would become with the advent of the computer. The principle of hiscalculations, published in a treatise concerning the propagation of heat in 1808, isapplied in many scientific software packages for the treatment of spectra (acoustical,optical or mass-spectrometric) and images. Legend has it that he was elaboratingthese calculations when Napoleon’s army requested him to improve the dimensionsof their cannons. In general terms, a transform is a mathematical operation thatpermits data to be changed from one type of measurement to another (for example,from time, to wavelength).

This FTIR technique of obtaining spectra, also adapted to the near-IR, hassignificantly modified traditional procedures of obtaining IR spectra. Adopted byalmost all manufacturers of spectrometers (e.g. see Figure 10.10) this method hasseveral advantages:

• the entrance slit is replaced by an iris furnishing a better signal to the detectorwhich receives more energy (multiplexing advantage);

• the signal-to-noise ratio is much higher to that of the sequential method since itcan be improved by the accumulation of successive scans (Fellgett advantage);

Figure 10.10 Fourier transform infrared spectrophotometer. The optical bench of the 380 FTIR,equipped with a diamond ATR accessory (reproduced courtesy of Nicolet).

10.8 SOURCES AND DETECTORS USED IN THE MID-IR 221

• the wavelengths are calculated with higher precision which facilitate thecomparison of spectra;

• the resolution is better and constant across the entire region under study.

There exists another way, chosen by a few manufacturers, to incorporate a delayinto one of the optical paths when obtaining an interferogram. The principlerelies upon the light passing through a crystal having two refractive indices, whichconstitutes a polarization interferometer.

10.7.2 Infrared analysers

Numerous autonomous small-sized instruments, used for analyses relating topersonal protection and other specific targeted applications, are based uponabsorbance measurements in the mid-IR or in the near-IR. Sensitivity, rugged-ness and easy-to-use are important features for process installations. Designed toquantify one or many compounds from very weak absorbances �1×10−5�, theyare able to measure reliably concentrations of the order of ppm for gases such ascarbon monoxide and dioxide, ammonia, methanal, ethanol, methane, etc. (in totalaround hundred gases or volatile compounds). The source can be a laser diode,which emits at a precise wavelength or a simple filament with a silica covering(case of the breathalysers). While the principle is simple, the chemistry is sensitive.Measurements of the levels of carbon mono- and dioxide in motor car gas exhaustsare carried out by this method. CO is measured by recording the absorbance at2160 cm−1 (cf. Figure 10.5) while CO2 is measured at 2350 cm−1 (Figures 10.11and 10.12). For ethanol the characteristic absorbance of primary alcohols at1050 cm−1 is considered. These infrared colorimeters are competitive with instru-ments based upon other inventive solutions (e.g. amperometric detection cf.Chapter 20), which are not derived from common laboratory spectrometertechnology.

10.8 Sources and detectors used in the mid-IR

10.8.1 Light sources

In the mid-IR several type of sources are used. They are either a lamp filament(Figure 10.13), or a hollow rod, 1–3 mm in diameter and 2 to 4 cm long, madeof fused mixtures of zirconium oxide or rare earth oxides (Nernst source) heatedby Joule effect by the means of an internal resistor (for example Globar™).These sources are heated to 1500 �C, without a protective shield. They dissipatepower of the order of a hundred watts by emitting radiation over a large domainranging from visible to thermal IR. A maximum is observed for �= 3000/T (� in


0

50

75

100

25

2400 cm–1 2300 22002600 2500

Laser diodeF1

F2 D2

D1Gas flow cell with a fixedand direct optical path

% T

F1 F2

Source

CO2 4.23 (2364) 1.96CH4 3.26 (3067) 1.65NH3 10.3 (971) 1.50HCHO 3.55 (2817) 1.93

gas μm (cm–1) μm

mid-IR near-IR

Figure 10.11 Non-dispersive analyser for measuring CO2 in gaseous media. This assembly isrepresentative of many portable detectors. The selectivity is assured by an adapted optical filter(F2) and by a membrane at the entrance to the cell which only permits gas to pass through tothe detector. The assembly contains a second filter (F1) chosen in a non-absorption zone whichauthorizes to a computation of the transmittance. On the diagram are shown the bandwidths ofthe two filters and the spectrum as function of transmittance of a gas, here CO2. The detectorsare thermistors. Left, a chart which presents a choice of wavelengths in the mid-IR and the nearIR for several gases (reproduced courtesy of Edinburgh Sensors, GB).

micrometres and T in Kelvin – adapted from Stefan’s law). The intensity of theradiation varies enormously as a function of the temperature of the source.

10.8.2 Detectors

The detection of photons in the infrared region was difficult to achieve for along time and a major cause of this was the mediocre sensitivity of the firstspectrophotometers.

The principle relies upon the thermal effect of IR radiation. Sensors that measureradiation by means of the change of temperature of an absorbing material areclassified as thermal detectors. They respond to any wavelength radiation thatis absorbed and can be made to cover a wide range of wavelengths. Numerousdevices have been used, thermistors, thermocouples, thermopiles and other sensorsrather imaginative (Figure 10.12b). For FTIR instruments, one of the mostcommon thermal sensors is the pyroelectric detector. It has a rapid time responseto follow the variations of light intensity, a weak thermal inertia and a linearresponse. Other detectors are photo-diodes (Figure 10.14) and diode arrays that

10.8 SOURCES AND DETECTORS USED IN THE MID-IR 223

Gas sample analysed

Gas sample analysed

M

1 - IR source (900 K)2 - Measuring cell3 - Reception chamber4 - Equilibration chamber5 - Microflow probe6 - Motorised shutter7 - KBr window

1 2 3 4

56

V V1 V2

(b)

(a)

SA

F C D

L

RAxCx

ARCR

X

7 7 7

.

Figure 10.12 Two models of single beam gas analysers. (a) The light issuing from the source S,crosses first a cylindrical assembly serving as a modulator which contains two capsules one R,filled with the gas to be detected and the second A, with a neutral gas (nitrogen). Next, the lightpasses through an interferential filter F chosen as a function of the wavelength at which themeasurement will be made, then cell C containing the sample. When the cell R is in the pathway,a known supplementary absorbance is obtained which allows a deduction of the absorbance dueto the gas under study (and the interfering compounds) in the measuring cell (adapted froman instrument of Servomex, GB); (b) the light from the source, after having passed through themeasuring cell reaches the cell V1 containing the reference gas (for measuring CO for example,V1 and V2 contain this gas). The measuring of the gaseous flow, by a microflow rate, analyser,circulating between V1 and V2 gives an indication of the variations of pressure between thesetwo chambers and therefore of the infrared radiation absorbed by the gas present in V1: Theradiation reaching V1 will be all the more attenuated when the sample in the flow cell V willcontain this same gas. A beam-chopper serves to break up the light flux to create a pulsed signal(adapted from an instrument of Siemens).

are capable of delivering a full infrared spectrum over a pre-defined wavelengthrange.

The pyroelectric detector contains a mono-crystal of deuterated triglycinesulfate (DTGS) or lithium tantalate �LiTaO3�, sandwiched between two elec-trodes, one of which is semi-transparent to radiation and receives the impact ofthe optical beam. It generates electric charges with small temperature changes.The crystal is polarized proportionally to the radiation received and it acts as acapacitor.

The photodiode detector contains a semiconductor, which is used either inphotovoltaic mode (no voltage ramp) or in photoconductor mode (with voltageramp) and contains a P–N junction, which, under the effect of radiation,liberates electron/hole pairs which create a PD measurable in an open circuit.


1 cm

Inte

nsity

(ar

bitr

ary

units

)

Spectrum of a SiC sourcetaken with a DTGS detector

Wavenumber (cm–1)

60

80

40

100

20

050001000015000

T = 1273 K

Figure 10.13 Typical emission spectrum of a mid-IR source along with a basic design of a source.In dotted lines is represented the theoretical emission curve of a perfect source (‘black body’radiation at 1000 �C). According to the model of source, of the beam-splitter and of the detectorbeing used, an experimental curve is registered which appreciably differs from the theoreticalcurve. It is noticed in particular that between 4000 and 400 cm−1, the signal intensity is dividedby a factor ten approximately. Current sources are robust and have a many years’ life expectancy.

Pyroelectric detector Photoconductive detector

IR

Crystal

Blackened face

Potential drop Potential drop

Semi-conductor

Quartzsubstrate

Voltage(bias)

Window

sensitiveelement1–3 mm

R

Connections Quartzsupport

Electrodes

1 3 4 40μm

DTGSMCT

PbS0.2 0.6

2 5

Figure 10.14 Detectors in the infrared. The functioning principles of pyroelectric and semi-conductor detectors. Centre, general view of a detector and its container. Below, range of usesfor the principal detectors.

This type of detector is constituted, for the mid-IR region, of a ternary alloy ofmercury–cadmium telluride (MCT) or indium antimonide (InSb) deposited uponan inert support and for the near-IR of lead sulfide (PbS) or an other ternary alloyof indium/gallium/arsenic (InGaAs). Sensitivity is improved when these detectorsare cooled down to liquid nitrogen temperature of (77 K).

10.9 SAMPLE ANALYSIS TECHNIQUES 225

10.9 Sample analysis techniques

Spectra are acquired from samples either by transmission or reflection. This secondprocedure, now common in the infrared, is the fundamental way to meet theneeds of qualitative and quantitative techniques for the analysis of all kinds ofsolid or gaseous samples and aqueous solutions.

10.9.1 Optical materials

Traditional optical material used in the visible or the near-IR becomes opaquein the mid-IR. Other crystalline or amorphous materials, each one having itsparticular spectral range, must be used for the detectors windows and IR cells.There are more than a dozen. The most common are sodium chloride (NaCl) andpotassium bromide (KBr), already mentioned. To replace these fragile and watersoluble materials, caesium iodide (CsI is transparent up to 200 cm−1), silver chlo-ride (AgCl), the KRS-5 (thallium bromoiodide) and even diamond can be used.These last materials are hard and insoluble, but unfortunately more expensive.AMTIR (amorphous material transmitting infrared radiation), a glass composedof germanium, arsenic and selenium (e.g. Ge33As12Se55) is finally a good choice.

10.9.2 Transmission procedures

• Gases, for which the absorbances are weak, require cells for which the opticalpathway can be very long, at least of several centimetres (Figure 10.15) butsometimes reaching several hundreds of metres through a complex arrange-ment of mirrors giving multiple reflections of the infrared beam inside thecell. The cell volume then becomes important (0.2 L).

• In contrast, for the hyphenated techniques such as GC/IR threadlike gas cells(light pipes) whose volume does not exceed a few tens of microlitres (l=10 cmand diameter < 1mm) are used. These cells use gilded side walls to provokemultiple reflections.

• Liquids are usually analysed with cells, which have two dismountable IRwindows. For qualitative analysis, a droplet of the sample is compressedbetween two NaCl or KBr discs without spacers to create a film. For quan-titative analysis, depending upon the wavelength of the measurement, eitherquartz Infrasil™ cells (with optical pathway of 1 to 5 cm), or sealed cells thathave a variable or fixed path length (Figure 10.15), can be used. The opticalpath length must be calibrated and periodically controlled.

• Solids are more difficult to study. Some approaches are given below.


commercial gas cell andcell for liquid film

Teflon O-ring

IR window (ex. KBr)KBr window

Back plate

Pyrex glass cell body

IR window

Knurled end cap

Spacer

Figure 10.15 Cells in the mid-IR. View of the direct optical pathway for a gas cell and ofa simple cell for liquid films with a fixed path length (reproduced courtesy of Spectra Tech).The cell design for the mid-IR allows them to be dismantled, due to the nature of the materialchosen for their windows which requires replacement. By contrast, in the near-IR the cells areof quartz as in the UV/Vis.

If the solid can be dissolved in a suitable solvent, then the same method as for aliquid is followed although no solvent exists which is transparent across the wholerange of the mid-IR. This procedure permits of quantitative measurements to beperformed at all wavelength except those absorbed by the solvent.

Pellets are used for solid samples that are difficult to melt or dissolve in anysuitable IR-transmitting solvents. A few milligrams of the solid grinded to a finepowder (ideally to particles of less than 1�m), is dispersed in a medium which willplay the role of matrix, such as a paraffin oil (called Nujol™), or dry potassiumbromide (KBr). One obtains a mull or a pellet. The matrix leads to a reduction ofthe strong optical dispersion caused by the particle/air interface while maintainingthe solid in the optical path of the instrument. The finer the powder is groundthen the less light will be lost through scattering or diffraction.

Nujol presents three major absorption bands beyond which the spectrum of thesample is exploitable. This spectrum can be supplemented by another carried outin hexachlorobutadiene, transparent in the regions where paraffin absorbs. For theKBr technique, the sample is crushed with KBr in an agate mortar. The mixtureis then pressed using an hydraulic press (pressure of 5 to 8 t/cm2) or manuallyinto a transparent disc.


10.9.3 Techniques using reflection for solid samples

Obtaining spectra by reflection is an alternative to the procedures described above(see Figure 10.17). The corresponding devices are based upon attenuated totalreflection, specular reflection or diffused reflection and are only usable with FTIR asthe spectra obtained by reflected light must be corrected by computer software torender them comparable with transmission spectra.

When a light beam impacts at the surface of a medium for which the refractiveindex is different it can undergo, depending upon the angle of incidence and thevariation of the refractive index, either a total reflection as in a mirror, or anattenuated reflection after having in part penetrated into the second medium (justa few micrometres for the mid-IR). The spectral composition of the beam reflecteddepends of the compound studied and upon the way in which the refractive indexof the material varies with the wavelength.

Attenuated total reflection (ATR)

ATR consists of imposing on an optical beam one or several reflections at theinterface between the sample and a material upon which the sample has beendeposited. This material must be transparent in the region of the wavelengthchosen and to possess a high refractive index n such as germanium �n = 4�,AMTIR �n = 2�5�, diamond �n = 2�4� or KRS-5 �n = 2�4� (Figures 10.16 and10.17a).

If the angle of incidence is greater than the critical angle, the light penetrates thesample that corresponds to half a wavelength at each reflection. The penetrationis thus dependent upon the wavelength, the refractive indices of both the crystaland the sample and the angle of incidence. This is sometimes referred to as anevanescent wave. The succession of several total but attenuated reflections of thistype leads to an effective optical pathway comparable with that which would havebeen obtained through conventional transmission. The spectrum is neverthelesscorrected to take into account the depth of penetration which increases with thewavelength.

ATR requires little or no sample preparation for most samples. This procedurehas become indispensable for studying thick or highly absorbing solid and liquidmaterials, including films, coatings, powders, aqueous liquids and even gases. Insome devices the crystal is immersed into the solution being analysed. It is themost versatile sampling technique.

� Optical fibre probe. ATR is used for the study of samples at a distance fromthe optical bank of the apparatus through the use of suitable optical fibres, that is,


Focusing crystal(eg. ZnSe)

Total reflection

AttenuatedTotal Reflectionof the beam

Disk of diamondSample

Sulfuric acid 1M (sample)

Water (Sample)

Water, vapour at 250°C (dotted line)

Stand

Wavenumber

Abs

orba

nce

0

0,5

0,8

4000 3000 2000 1000

Wavenumber

3700 2700 22003200 1700 1200

Abs

orba

nce

Figure 10.16 ATR three reflection device and examples of spectra. The small diamond disc(diameter 0.75 mm) enables the isolation of the sample examined from the ZnSe crystal.Chemically inert and resistant, diamond is appropriate for examination of all sorts of hardsamples which are pressed against its surface or contain water. Above right, are reproduced twospectra obtained with such a device. Spectra obtained from a drop of sulfuric acid �H2SO41M�deposited as a sample (reproduced courtesy of SensIR). Below, spectrum of water at 25 �C andof heated water vapour (250 �C) (Intl Lab 32,(2), 2002).

transparent in the infrared over a distance of several metres. They can be used asimmersible probes plunged into the product to be analysed enabling rapid controlanalyses in difficult or aggressive environments.

Specular reflection

This accessory, which can only be used with FTIR spectrometers, is a non-destructive method reserved for samples which reflect at least a minimum of


Stand

model at 30° incidence model at 60° incidence

SampleSample

IR IR

Specular reflection(b)

(a)

SampleIR

Attenuated Total Reflection

Trapezoidal crystalMultiple path cell

n1n2

r

i

θ = 30°

sin r = (n2/n1)sin i with n1 > n2

θc θc

h

Ld

Ex. of crystal shapeL × d × h : 25 × 5 × 3 mm

Single path cell

ZnSe

Mass

Diamond

(c) Diffuse reflection

Optical pathway

Sample holder

to the detectorIR Source

Ellipsoidal mirror

Figure 10.17 Devices allowing the study of samples by reflection. (a) Schematic representationof two ATR devices (attenuated total reflection): a model with a trapezium crystal for multiplereflections and a model for single reflection with solid microsamples (the application of a weightimproves the contact of the sample with the crystal’s rounded form). Basic formula and notionof critical angle; (b) Specular reflection device. Optical pathway of the apparatus at a fixed angleof 30 � for highly reflecting samples and of 60 � for the contrary; (c) Optical scheme for a diffusereflection device and diagram of a Spectra Tech model.


light (polymer films, varnish and some coatings) and measures the reflectance,that is the light reflected by the sample in a direction parallel to that of theincident light (Figure 10.17b). The reflected light, which corresponds to only asmall part of the incident radiation, is modulated by the variations in the refrac-tive index of the compound as a function of wavelength. By comparing, foreach wavelength, the specular reflection I of the sample with the total reflectionI0 obtained by replacing the sample with an aluminium mirror, the instrumentcan calculate the reflectance spectrum R = I/I0 = f ��. Finally, by a mathe-matical transformation known as the Kramers–Krönig (K-K) theory, a pseudo-absorption spectrum is calculated, equivalent to one obtained by transmission(Figure 10.17b).

Diffuse reflection

This is a device containing a series of flat and elliptical mirrors arranged to collecta sufficient part of the light diffused by the sample finely dispersed as a powderin KBr (Figure 10.17c). By comparing the diffused reflection with that of neatKBr, a result resembling the classic transmission spectrum is obtained. A finalcorrection due to Kubelka–Munk is generally added to get a better spectrum. Verytime consuming, this technique has been all but abandoned.

Figure 10.18 compares these three approaches using two organic compounds.

10.10 Chemical imaging spectroscopy in the infrared

The high sensitivity of detectors allows the study by transmission or reflectionof very small samples such as those that can be examined under an opticalmicroscope. The focusing of the beam upon a zone of only a few micrometresenables to obtain a chemical map which is linked to the composition of thesample if it presents a microstructure. The instrumentation includes a spectrometercoupled with an observation microscope (Figure 10.19).

� Many industrial or natural compounds are heterogeneous solid mixtures. Tradi-tional methods giving averaged values for the atomic composition are sometimesinsufficient. Chemical imaging spectroscopy is a new analytical advance that answersasked questions as what chemical species are present and where are they located?For example, it is possible to study the dispersion of the active agent of a medicationwithin its excipient, or to evaluate the impurities in a foodstuff for cattle. Statisticalmethods and chemometric approaches as partial least square (PLS) or principalcomponent analysis (PCA) are then very useful in this context. Mid-IR and near-IR are also applied to observation of terrestrial giant samples using satellite-basedsensing systems and detectors as plane arrays.

10.10 CHEMICAL IMAGING SPECTROSCOPY IN THE INFRARED 231

Benzoic acidResolution: 4 cm–1

Transmittance spectrum

Benzoic acidResolution 4 cm−1

Diffuse reflection spectrum

Wavenumber (cm–1)

4000 2000 1500 10003000

Kubelka

Munk

Absorbance

0,0

0,4

0,4

0,0

CO2H

Benzoic acid(b)

40004000 20002000 450450

Abs

orba

nce Transmission

spectrumCO2Me

nMe

Methyl polymethacrylatePMMA

K K

K M

Corr.

Specular reflection

Diffuse reflection

Attenuated TotalReflection (ATR)

Abs

.P

seud

o A

bs.

KRef.

Ref.

(a)

Figure 10.18 Spectra by reflection. (a) From a sample of plexiglass, three types of reflection aredisplayed. Left, crude spectra and right, spectra after correction. Above, crude signal of specularreflection and the result in units of K following application of the Kramers–Kronig (transfor-mation of the reflectance) calculation; middle, spectrum obtained by diffused light: comparisonof the crude spectrum with the Kubelka–Munk correction; below, spectrum obtained by ATR,the latter requiring a fine correction to reduce the absorbance at higher wavelengths whichwould be overestimated; (b) comparison of two spectra of benzoic acid, one obtained throughtransmission, the other by diffused reflection and subsequent K-M correction.


Sample

Cassegrainlens

Cassegraincondenser

Towards detector

Variable aperture (iris)

Figure 10.19 FTIR imaging system. Left, an optical pathway in an IR microscope associatedwith a spectrometer. The sample can be examined in transmission (left), or in specular reflectionmodes (right). This accessory is installed in a spectrometer whose beam is deflected. TheCassegrain optic has the advantage that the light is reflected at the surface of mirrors ratherthan having to pass through optical lenses. Right, model 400 UMA (reproduced courtesy ofVarian Inc. USA).

10.11 Archiving spectra

Different methods are used to store spectra with less memory space than theoriginal files. The experimental data points are mathematically treated by aderesolution procedure in order to replace them by a smaller number of calcu-lated values (e.g. a point calculated each 4 or 2 cm−1 reduces a spectrum to lessthan 1 Ko). Another standard format is the JCAMP-DX (Joint Committee onAtomic and Molecular Physical Data) for exchange spectra in computer read-able form. It preserves all of the numerical values of the original spectrum, aswell as all of the related information regarding the spectrum in an ASCII file.Most FTIR spectrometers have JCAMP.DX import/export utilities. This format iscompatible with all of the comparison algorithms to enable further identification(Figure 10.20).

Coupled techniques such as GC/FTIR and HPLC/FTIR require that chro-matograms are displayed in real time on the screen. Consequently, the mobilephase exiting the column is sampled at very short time intervals throughout theelution. IR spectra must be calculated rapidly. They serve to construct a ‘pseu-dochromatograms’ called Gram–Schmidt according to the mathematicians whosemethod is used to treat the data. The individual IR spectra are obtained in differedtime (Figure 10.21).

10.12 COMPARISON OF SPECTRA 233

.....(missing values)....

##TITLE= CAFFEINE ##JCAMP-DX= 4.24 ##DATA TYPE= INFRARED SPECTRUM ##ORIGIN= EPA1100.SPC$$converted Galactic SPC file##OWNER= EPA FT-IR Vapor Phase Library ##DATE= 05/05/05 ##TIME= 09:47:00##MOLFORM= C 8 H 10 N 4 O 2 ##CAS REGISTRY NO= 58-08-2##NPOINTS= 1842 ##XUNITS= 1/CM ##YUNITS= TRANSMITTANCE ##RESOLUTION= 1.93055##FIRSTX= 449.413##LASTX= 4003.553##XFACTOR= 1.0##YFACTOR= 5.9604E-8##FIRSTY= 99.311##MAXY= 100.92 ##MINY= 7.9067 ##XYDATA= (X++(Y..Y))449.41 1666172247 1662340156 643311506 1635761175 1628245537460.99 1617036772 1605905171 1598526705 1580228522 1562139796 1547818013472.57 1537162907 1540706434 1537162907 1540706434 1558546974 1572968030

1658516880 1

3959.1 1681589144 1681589144 1685465608 1685465608 1685465608 16893510083970.7 1689351008 1689351008 1689351008 1689351008 1689351008 16893510083982.3 1689351008 1689351008 1689351008 1685465608 1685465608 16854656083993.8 1685465608 1685465608 1685465608 1681589144 1681589144 1681589144

Figure 10.20 Example of a JCAMP-DX file read by a word processor. This type of file enablesthe reproduction of the original spectrum by treatment with a suitable software. Experimentalpoints are arranged in sequences of six data points. Only the beginning and the end of the filehave been retained.

Wavenumber (cm–1)

Tim

e (m

in)

Glucose

Sucrose

Fructose

9

10

16

Abs

orba

nce

0,01.

1400 1300 1200 1100 1000 900

0,02

0

0,03

Figure 10.21 Gram–Schmidt process. Three-dimensional pre-recorded reconstruction between1400 and 900 cm−1 of a solution containing 10 mg/mL of three sugars, saccharose, glucose andfructose, by HPLC/FTIR (volume injected = 50�L) from Keller R. et al. 1997 Anal Chem 69,4288.

10.12 Comparison of spectra

One of the most positive identification methods of an organic compound is tofind a reference IR spectrum that matches that of the unknown compound. Thisapproach is facilitated using spectral libraries as compiled by various societies or


editors (e.g. Aldrich, Sigma, Sadtler, Hummel), whether generalized or specialized(polymers, solvents, adhesives, organic molecules classed by functionality). Inorder that the comparisons are reliable, these data collections should have beenobtained from compounds in the same physical state as the compound to beidentified (‘EPA Vapor-Phase IR’ for example, when the method is GC/FTIR).The archived spectra are normalized by attributing to their most intense band anabsorbance value equal to one.

The spectrum to be compared must first be adjusted to conform (absorbanceand wavelengths) with the model of the spectra in the library. Then the procedureconsists of a mathematical comparison of the unknown compound’s spectrumwith all those included in the spectral library in order to establish, by the endof the research session, a list of spectra that most resemble that of the unknowncompound, each having an index of reliability. The analyst must examine theseresults with attention recalling that the objective of this exercise is to aid and notto substitute for, because if the algorithm for comparison is changed, the finallisting will be probably different. The best methods of identification are associatedwith interactive programs in which the analyst contributes information in orderto narrow the field of investigation, by defining filters.

The algorithm using the absolute difference is the simplest: for each of thej spectra in the library the sum Sj , for the n defined points along the abscissa,is calculated as the absolute difference between the corresponding absorbance ofthe unknown and that of spectrum j in the library (expression 10.10). Then thej summations Sj are classified in increasing order. The results are presented alongwith an index of correlation.

SJ =n∑

i=1

∣∣∣yref �J�i − yinc�

i

∣∣∣ (10.10)

Other expressions can be chosen: replacing the differences above by their squaresor by the differences of these squares or taking the incremental difference betweentwo consecutive points. Each algorithm may minimize or increase the value ofparticular factors (differences of intensity, signal-to-background improvement,difference in gradient � � � ).

10.13 Quantitative analysis

The precision of absorbance measurements and the possibilities of storage andre-treatment of the spectra have favoured quantitative analysis by infrared. Themethod is widely used for the facility with which the absorption bands of aparticular compound can be located even in a mixture and because efficientmethods of statistical analysis are available for the near IR. However, the develop-ment of reliable FTIR instrumentation and strong computerized data-processingcapabilities have greatly improved the performance of quantitative IR work. Thus,

10.13 QUANTITATIVE ANALYSIS 235

modern infrared spectroscopy has gained acceptance as a reliable tool for quanti-tative analysis.

In the early ages of FTIR, some analysts considered that double beam dispersiveinstruments were preferable for quantitative analysis as they are the only ones tocompare the intensities transmitted by the two pathways (of reference and sample)at the same instant.

10.13.1 Quantitative analysis in the mid-infrared

For solid samples dispersed in a KBr disc the thickness of which cannot bemeasured with precision, a compound is introduced as an internal standard(calcium carbonate, naphthalene, sodium nitrite), in an equal quantity to all ofthe standards as well as to the sample.

For liquid and solutions, the absorbance measurements are carried out in cellsof short optical path l to minimize absorption by the solvent, of which none arereally transparent in this spectral domain. The uncertainty in the value of l islinked to the softness of the material used for the construction of cell windows.This means the periodic calibration of their optical path.

The exact measurement of the optical path in cells of low thickness is madeby interferometry (interference pattern method). The transmittance of the emptycell is measured for an interval between two wavenumbers �1 and �2 (in cm−1).Figure 10.22 shows that the beam S2 has undergone a double reflection from theinternal walls of the cell, thus for a normal incidence, there would be, if 2l = k�,addition of both light intensities (the two beams S1 and S2 are in phase). As afunction of the wavelength a modulation of the main beam S1 of a few percentis observed. After calculation, if N represents the number of interference fringescounted between �1 and �2 (in cm−1), then:

l�cm� = N

2��1 − �2�(10.11)

85

80

75

1200 1100 1000 900 cm–1

%T

IR Source S1

S2⎢

Figure 10.22 Measurement of cell thickness by the method of interference fringes. Left, reflectionson the inner wall of a cell (for further clarity, the angle of incidence of the beam on the cellis shifted from normal incidence by a small angle). Right, part of the recording obtained froman empty cell. Twelve fringes are counted between the two arrows. The calculation (expression10.11) using this data leads to a cell path-length of l = 204�m.


Wavenumber (cm–1)1500 1000

0.30

0.25

0.20

0.10

0.15

0.05

0

Abs. Units

Figure 10.23 Correction of the absorption baseline. In supposing, for the given example, thatthe measurement of the concentration is based upon the absorbance of the band at 970 cm−1,then it will be necessary to deduct from the total absorbance (0.29 AU), the baseline absorptionof 0.05 AU which leads to 0.24 AU.

Also to be taken into account is the background absorption which is often visiblefor a substantial part of the spectrum. In particular it depends upon the mannerin which the sample has been prepared. As absorbances are additive, that not dueto the compound under study must be subtracted from the total absorbance. Thisis evaluated by the tangent method (Figure 10.23).

10.13.2 Quantitative analysis in the near infrared

The absorption bands in the near-IR originate from harmonics or combinationsof the fundamental vibrations present in the mid-IR.

� From this point of view the water molecule has been particularly well studied.To a first approximation the band which appears around 5154 cm−1 (1940 nm, seeFigure 10.24) results from the combination of the asymmetrical vibration situated at3500 cm−1 and the deformation vibration (scissoring, see Section 10.6) at 1645 cm−1

(Figure 10.16). These simple calculations (3500 + 1645 = 5145) are an imperfectapproach, which conceals a certain number of factors of the physical state of thecompounds to which infrared is sensitive. Among the approximations are those forthe combination bands of the bonds C–H, N–H and C–O in the near-IR.

In this region, essentially reserved for control analyses and where the crudespectra are fairly often disconcerting due to the absence of clear absorption bands,a method employing standards and based upon a single wavelength as in UV/Visspectrometry can rarely be used (cf. Chapter 9). For many samples, as in thecomplex matrices of the agricultural and food industries, calibration and validationmethods require a great number of representative reference samples, themselvesmeasured by a proven method (Kjeldhal, for example, for the protein nitrogen).

10.13 QUANTITATIVE ANALYSIS 237

Arb

itrar

y un

its

Wavelength (nm)

1900 2100 2300 25001100 1300 1500 1700

Pure water (sample)

Mixture 50 : 50 methanol/water

0

0

Figure 10.24 Derivative plots. Comparison of graphs of the second derivative of pure waterand of a mixture of half water/half methanol in the near-IR. Note that it is possible to measureout the methanol from the peak situated around 2�3�m without interference from the watersignal located at 1�94�m. In this spectral region, considered as an extension of the visible range,the wavelengths are rather expressed in nm or �m.

In this way, correlations with around 50 reference samples, very similar to those tobe measured, is not unusual. Many products (proteins, oils in cereals, meat), canroutinely be analysed by this method and often without preparation beforehand.In general, a relation is sought between certain absorptions and the presence ofconstituents in the mixtures to be analysed. This is the domain of correlationanalysis.

As the absorption bands are not very intense, the measurements are under-taken with cells of 1 cm optical path-length and on undiluted sample. They areaccomplished either in transmission or reflection (for example, proteins, fats, cellu-lose or starch are measured by reflectance). By using derivative plots, precision isimproved (Figure 10.24).

Some application software programs use methods known as MLR (multiplelinear regression) that permits the statistical treatment of a large number of datapoints in order to establish a calibration equation. These chemiometric methodstake advantage of all the absorptions measured at different wavelengths, irrespec-tive of their origin: analyte to be measured, matrix or artefacts of the instrument.


PCA and PLS methods are commonly used. In conclusion, although certainmeasurements in the near-IR are not always very sensitive, they are reputed to bevery reliable.

Problems

10.1 1. What is the energy possessed by a radiation of wavenumber 1000 cm−1?

2. Transform � = 15�m into units of cm−1 and then into m−1. What isthe wavelength corresponding to a wavenumber of 1700 cm−1?

3. At the maximum of an absorption band, the transmittance is only 5%.What is the corresponding absorbance?

10.2 If chloroform (trichloromethane) exhibits an infrared peak at 3018 cm−1 dueto the C–H stretching vibration, calculate the wavenumber of the absorptionband corresponding to the C–D stretching vibration in deuterochloroform(experimental value 2253 cm−1).

10.3 A ketone possesses an absorption band with a peak centred around1710 cm−1. From this information deduce a value for the force constant ofthe C=O double bond.

10.4 The bond between the two atoms of a diatomic molecule is characterisedby a force constant of 1000 N/m. This bond is responsible for a vibrationalabsorption at 2000 cm−1. Accepting that the energy of radiation is trans-formed into vibrational energy, estimate a value for the length of the bondat the maximum separation of the two atoms.

10.5 The examination of an absorption band located around 2900 cm−1,expressed by a sample of HCl in the gaseous state, reveals that the bandis the result of a superimposition of two forms of vibration, one of whichis clearly more intense than the other. These two series are separated byan approximate distance of 2 cm−1. How might this phenomenon be inter-preted? Use calculations to illustrate your answer.

PROBLEMS 239

10.6 Knowing that the fundamental frequency of carbon monoxide is 2135 cm−1

when the spectrum is recorded with tetrachloromethane as the solvent,calculate the force constant of this molecule under these conditions.

10.7 The following experiment is used to determine the vinyl acetate (VA) levelin an ethylene vinyl acetate (EVA) commercial packaging film.

Infrared spectra of packaging films with known vinyl acetate contents arerecorded. The absorbance peak at 1030 cm−1 used to determine the contentof the vinyl acetate was measured by the baseline method �A = log�I0/I�.The following results were obtained.

(EVA) %VA A1030 A720 d��m�

1 0 0�01 1�18 562 2 0�16 1�55 803 7.5 0�61 1�49 824 15 0�36 0�45 27

1. Taking into account the film thickness, determine, from the data inthe table, the best line A1030 = f�% VA�, using linear regression, fora film thickness of 1�m.

2. Explain why the polyethylene peak at 720 cm−1 may be chosen asan internal standard, then calculate the ratio A1030/A720 for the fourfilms.

3. Using both above methods calculate the vinyl acetate content (%)of an unknown EVA film (giving d = 90�m, A1030 = 0�7 andA720 = 1�54).

10.8 1. In supposing that the signal to noise ratio obtained for an FTIR is 10for a signal corresponding to a single scan, what would be the expectedvalue following 16 scans?

2. The resolution (in cm−1) is given by the expression R = 1/, where represents the difference of the maximum optical path between thetwo beams (in cm) when the mirror glass is moving. What must be thedisplacement of the mirror relative to the central position to obtain aresolution of 1 cm−1? (The central position of the mirror is such that�, the difference between the optical paths, is zero.)


3. To locate the position of the moving mirror with great precision, wesuperimpose in the apparatus a laser source of monochromatic radiation�� = 15 800 cm−1�, which permits a computer to pick up a point of theinterferogram each time the laser light is extinguished.

What, in �m, is the value of the displacement dx of the mirrorbetween two successive extinctions of the laser beam’s light?

11Fluorimetry andchemiluminescence

Some organic or inorganic compounds, liquids or solids (molecular or ionic crys-tals), whether pure or in solution, emit light when they are excited by photonsfrom the visible or the near ultra-violet regions. Among the analytical applica-tions of this phenomenon, known as photoluminescence, is fluorimetry, a selectiveand highly sensitive method for which a wide range of measurements are acces-sible. The intensity of the fluorescence is proportional to the concentration ofthe analyte and the measurements are made with the aid of fluorometers orspectrofluorometers. The extremely rapid extinction of the light intensity whenexcitation ceases is the object of analysis. By contrast, phosphorescence is char-acterized by a more gradual diminution during time. Fluorescence is equallyemployed as the basis of detectors used in liquid chromatography. Although ofdifferent origin, chemiluminescence which comprises the emission of light duringcertain chemical reactions, has also received several applications in analyticalchemistry.

11.1 Fluorescence and phosphorescence

Many compounds, when excited by a light source in the visible or near ultra-violet regions, absorb energy which is nearly instantaneously re-emitted in theform of radiation. According to Stokes’ law, the maximum of the spectral emis-sion band is located at a longer wavelength than that of the original excitationlight. These are fluorescent compounds (Figures 11.1 and 11.2). After excitation, thelight intensity decays extremely rapidly according to an exponential law. Expres-sion 11.1 links the intensity of fluorescence It and the time passed t since theexcitation:

It = I0 · exp �−kt� (11.1)


242 CHAPTER 11 – FLUORIMETRY AND CHEMILUMINESCENCE

Abs

orba

nce

Flu

ores

cenc

e

Wavelength (nm)

Absorption Fluorescence

235 285 335

H2C

H2C

HCH2C

CH2

C C

CH2CH

Figure 11.1 Representation on the same graph of the absorbance and fluorescence spectra ofan ethlyenic compound. The fluorescence spectrum that resembles the mirror image of theabsorbance spectrum, as well as the ‘Stokes shift’ can be interpreted by considering the energydiagrams (Figure 11.2). In UV/Vis absorption and fluorescence spectra, bandwidths of 25 nm ormore are common. This representation is obtained by uniting on the same graph, with a doublescale, the spectrum of absorbance with that of emission. Example extracted from Jacobs H.et al., Tetrahedron 1993, 6045.

This emission can be classified as fluorescence, which has a very rapid decrease inintensity or phosphorescence, where emission decay is much slower. The differencebetween the two is characterized by the value of the constant k, which for fluores-cence is much greater than for phosphorescence. The lifetime of fluorescence �0 isdefined, using the rate constant k, by �0 = 1/k. At the instant �0, the intensity It

will become, according to expression 11.1, 36.8 per cent of the initial intensity I0.In other words a fluorescent compound corresponds, on the microscopic scale,to a population of individual species of which 63.2 per cent have relaxed to annon-emissive state after this brief period of time.

Fluorescence lifetimes �0 are only a few nanoseconds. To facilitate the measure-ments of fluorescence, current instruments operate in a stationary regime, thatis the source of excitation is maintained illuminated, though with the oblig-atory discrimination between the light from the source and that due to thefluorescence. Figure 11.1 illustrates for example, the apparent mirror symmetryof the absorbance and fluorescence spectra that are common for numerouscompounds.

� Fluorescence can be resolved over time. The use of very short pulsed light sources(picosecond lasers and laser diodes) has rendered accessible graphs of fluorescencedecay as a function of the time. New applications based upon a greater knowledge ofthe lifetime are under development, although they are still not used much in chemicalanalysis.

11.2 THE ORIGIN OF FLUORESCENCE 243

11.2 The origin of fluorescence

Subjected to excitation by light, a molecule (the solute, initially in the ground stateS0), is instantaneously promoted to its first electronic excited state S1 (Figure 11.2).The electrons and those of the neighbouring solvent molecules re-equilibrate veryquickly; however the position of the atomic nuclei remains identical to howthey were in the fundamental state (this is the Franck–Condon principle). Thesolute/solvent cage system being out of equilibrium, will adopt a more stableconformation relative to the electronic excited state S1. Then, by the process ofinternal conversion, the molecule will rejoin �10−12 s�, without emitting photons,the state V0 of level S1. If this level is compatible with the fundamental level thesystem can relax through a fluorescent step (10−11 to 10−8 s) during which themolecule returns to one of the vibrational states of the ground electronic state S0

with emission of photons as fluorescence.Over the course of fluorescence that accompanies the return to the initial state,

the molecule can retain a part of the energy absorbed in the form of vibrational

Absorption Fluorescence Phosphorescence

E

S0 S0

T1

V1

V2

V0

V3

V4

V1

V2

V0

V3

V4

S1

Non-radiativedeactivation

(Vibrationalrelaxation)

Figure 11.2 Energy diagram comparing fluorescence and phosphorescence. The short arrows corre-spond to mechanisms of internal conversion without emission of photons. The fluorescence resultsfrom transfers between states of the same multiplicity (same spin state) while the phosphorescenceresults from transfers between states of different multiplicity. The state T1 produces a delay inthe return to the fundamental state, which can last several hours. The ‘Stokes shift’ correspondsto the energy dissipated in the form of heat (vibrational relaxation) during the lifetime of theexcited state, prior to photon emission. The real situation is more complex than this simplifiedJablonski diagram suggests. To our scale, a compound can be both fluorescent and phosphorescentfor, at the molecular scale individual species do not all exhibit the same behaviour.


Biphenyl (0.2) Fluorene (1)

NH2

Aniline (0.6)

Naphthalene (0.55)

8-Hydroxyquinoline

N

OH

Fluorescein (0.92 in NaOH 0.1 Mand 0.65 to pH = 7)

COOH

OOHO

Figure 11.3 Fluorescing aromatic compounds. The names are followed by their fluorescencequantum yield �f (cf. Section 11.3), for which the values are obtained by comparison withcompounds of known fluorescence. The measurements are made at 77 K. 8-Hydroxyquinolineis representative of various molecules forming fluorescent chelates with certain metal ions.

energy. This excess of vibrational energy is dissipated through collisions or othernon-radiative processes known collectively as mechanisms of vibrational relaxation.The emission of lower energy photons can equally be produced and be the originof a fluorescence in the mid-infrared.

Phosphorescence corresponds to one another relaxation process. After the absorp-tion phase, corresponding to the transfer of an electron into the S1 level (singletstate), an electron spin inversion can occurs if the vibrational relaxation is slowenough, which leads to a slightly stable T1 (triplet state). From here return to theground electronic state is slowed as it requires a new spin inversion for this elec-tron. These radiative lifetimes can be up to several minutes duration (Figure 11.2).

Sensitivity in fluorimetry is often 1000 times greater to that of the UV/Visabsorption. However, the correct use of these techniques requires a sound knowl-edge of the phenomenon in order to avoid a number of errors.

Fluorescence, which is often encountered with rigid cyclic molecules possessing�-bonds, is enhanced by the presence of electron-donating groups while beingreduced by electron-withdrawing groups (Figure 11.3). Equally, there is a depen-dency upon the pH of the solvent. In contrast, non-rigid molecules readily losetheir entire absorbed energy through degradation and vibrational relaxation.

� By analogy, this phenomenon can be compared with the effect produced whena hammer hits a block of rubber for example, or by opposition on something hardsuch an anvil. With the rubber, the energy is dissipated into the mass (as heat) andsound will not be emitted. Alternately on the anvil, a part of the mechanical energy istransmitted towards the outside (as sound waves) and this can be compared to thephenomenon of fluorescence of non-rigid vs. rigid molecules.

11.3 RELATIONSHIP BETWEEN FLUORESCENCE AND CONCENTRATION 245

11.3 Relationship between fluorescence andconcentration

At each point of the solution the intensity of fluorescence is different because a partof the excitation radiation is absorbed before reaching the point being consideredand because a part of the emitting radiation light finds itself trapped before itcan exit the cell. Globally the fluorescence received by the detector corresponds tothe sum of the fluorescence emerging from each of the individual small volumesconstituting the space delimited by the entrance and exit slits (Figure 11.4). Thisis why the calculation of the absolute fluorescence intensity (emission If ) forthe sample is difficult. The phenomenon of radiation damping, called internalquenching is due to the partial overlap of the absorption and emission spectra(colour quenching), and is increased by transfers of energy from excited speciesto other molecules or ions through collisions or complexes formation (chemicalquenching). That is why the presence of oxygen can cause an underestimation offluorescence.

For solutions, the quantum yield of fluorescence �f (between 0 and 1 inclusive),which is independent of the intensity emitted by the light source, is defined by theratio of the number of photons emitted to the number of photons absorbed, thislatter being equivalent to the ratio of fluorescence intensity If over that absorbedIa (expression 11.2).

�f = number of photons emitted

number of photons absorbed= If

Ia

(11.2)

Accepting that Ia = I0 − It (It representing the transmitted light intensity), thefollowing reasoning allows to relate If to the concentration C, of the compound:

If = �f �I0 − It� that is If = �f · I0 · �1 − It

I0

� (11.3)

I0 IFInternal filter

Pre-filter

c

a b

Figure 11.4 Intensity of fluorescence and radiation damping. Depending upon the site in thesolution where the fluorescence is emitted, a variable intensity of light reaches the detector. Byspecific positioning of the entrance and exit slits, it is possible to evaluate the re-absorption ofthe light of fluorescence (comparison between a and c) and the absorption of the incident light(comparison between a and b). In practice, the presence of an iris means that only the lightarriving from the central region of the cell is collected.


Concentration (arb. units.)

Fluorescence intensity

1

2

3

4

5

00 0,02 0,06 0,08 1,0

250 nm 500 250 nm 500250 nm 500

0.45 M/L0.15 M/L

0.015 M/L

1 unit1 unit1 unit

prefilterl1ε1λ1

internal filterl2ε2λ2

l

l

Figure 11.5 Intensity of fluorescence and concentration. Modelling of expression 11.7 revealsthe effect of the concentration upon fluorescence intensity. A maximum of fluorescence isobserved beyond which, with a continuing increase in concentration, it diminishes. After themaximum the more concentrated the solution then the weaker is the fluorescence – a kind ofroll-over or self-quenching. The illustrations correspond to three recordings, at the same scale ofbiacetyl tetrachloromethane. The curve records the light collected from a small volume situated atthe centre of the solution as indicated on Figure 11.4 (parameters and l chosen arbitrarily).

Knowing that the absorbance A is equal to log I0/I , expression 11.3 becomes:

If = �f · I0 · �1 − 10−A� (11.4)

with

10−A = 1 − 2303A + �2303A�2

2! − · · + · ·If the solution is diluted, the term A is close to 0 and the term 10−A is thereforeclose to 1 − 23A. The expression (11.4) can then be simplified, becoming:

If = 23 · �f · I0 · A thus If = 23 · �f · I0 · · l · C (11.5)

with I0 the intensity of the excitation radiation, C the molar concentration ofthe compound, its molar absorption coefficient, l the cell thickness and �f thefluorescence quantum yield.

11.4 RAYLEIGH SCATTERING AND RAMAN BANDS 247

This last expression reveals that the intensity of fluorescence depends uponthe concentration �C�, the experimental conditions �l� I0� and of the compound��f �. If all the parameters due to the instrument and most due the compoundare factored into a global constant K, then the following equation can be used forweak concentrations �A < 001�:

If = K · I0 · C (11.6)

Measurements by fluorimetry make use of several classic methods employingone or more standards (single point calibration or calibration curve, or methodsof addition), but to obtain the best results, the solutions must be very dilute.

Above a given limit, fluorescence is no longer directly proportional toconcentration. This arises because of the non-linearity of the Lambert–Beerlaw. The excitation is proportionally weaker and association complexes appearbetween excited molecules and those in ground state. This leads to the appar-ently paradoxical result that the fluorescence can diminish even though analyteconcentration increases. The curve in Figure 11.5 is a graphic illustration ofexpression 11.7 following the introduction of reasonable values for these differentparameters.

If = � · k · I0 · 10−�1�1 +2l2�C · �1 − 10−lC� (11.7)

11.4 Rayleigh scattering and Raman bands

When the wavelengths of excitation and of emission are close together then aconfusion becomes possible between the fluorescence of the sample and twoartefacts due to the solvent: Rayleigh scattering and Raman diffusion. The limitsof detection in fluorescence are often governed by the ability to distinguish theanalyte fluorescence from these additives interferences.

11.4.1 Rayleigh scattering

Rayleigh scattering is the re-emission, by the solvent in which the compound isdissolved, of a small fraction of the absorbed excitation light in all directions atthe same wavelength (Figure 11.6). The Rayleigh scattering intensity depends uponthe polarizability of the solvent molecules.

11.4.2 Raman diffusion

Raman scattering, which is 100 to 1000 times weaker than that of Rayleigh scat-tering, is produced by the transfer of a part of the excitation radiation energy to


Raman diffusion

Wavelength

Inte

nsity

(ar

bitr

ary

units

) Rayleigh scattering(Excitation line)

Diffracted light(2nd order of the grating)

Fluorescence

200 300 400 500

100%

Raman peakwater397nm

Rayleigh350nm

5%

Figure 11.6 The diverse components of a fluorescence spectrum. The position of the Ramanpeak depends upon the wavelength of the excitation beam and of the solvent. Right, a sensitivitytest for a fluorometer.

the solvent molecules in the form of vibrational energy. The solvent moleculesre-emit photons of less energy than those having served to excite them. Comparedto Rayleigh scattering, the Raman emission band is shifted towards longer wave-lengths. For each solvent the difference in energy between the absorbed photonsand the re-emitted photons is constant. Therefore it is possible, by modifying theexcitation wavelength, to displace the shift in nanometres between the position ofthe Raman and Reyleigh bands (Table 11.1 and Figure 11.6).

The Raman scattering of water serves as a sensitivity test for fluorometers. Thisconsists of measuring the signal/noise ratio of the Raman peak with a cell filledwith water, for example at 397 nm if the excitation wavelength is fixed at 350 nm,as a result of the specific shift of 3380 cm−1 for this solvent, and to compare withthe background signal.

Table 11.1 Position of the Raman scattering band, calculated for four commonlyused solvents and five excitation wavelengths from a mercury lamp

Excitation (nm) 254 313 365 405 436 Shift �cm−1�

Water 278 350 416 469 511 3380Ethanol 274 344 405 459 500 2920Cyclohexane 274 344 408 458 499 2880Chloroform 275 346 410 461 502 3020

� The phenomenon of fluorescence is not only used for chemical analyses but isequally applied to substances such as washing powders where a fluorescing agentthat sticks to the textile fibres is added. This type of compound absorbs solar radiationin the non-visible part of the spectrum and re-emits at longer wavelength, in the bluespectral region of the spectrum, visible to the eye, which makes clothing appears‘whiter’.


11.5 Instrumentation

A fluorescing compound behaves like a source which emits light in all directions.This emitted light is usually monitored in a direction perpendicular to the beamcoming from the primary excitation source. For strongly absorbing solutions,fluorescence is viewed from the face of the sample on which the exciting radiationimpinges, while for opaque or semi-opaque samples a frontal measurement ispreferable (Figure 11.7).

The excitation source is often a xenon arc lamp with a power of 150 to800 watts. The measurement of the light intensity is carried out using a photo-multiplier tube or a photodiode. The solvent, the temperature, the pH and theconcentration are the principal parameters which affect the intensity of fluo-rescence. For solution samples, rectangular 1 cm glass or fused silica cuvettesare used.

� Among the numerous applications of LIDARS (light detection and ranging),they are used for gas monitoring, only present as traces in the Earth’s atmo-sphere. Gases are quantified by their retro-scattering fluorescence which is inducedfollowing excitation by a very short pulse (1 μs) from a strong monochromatic laser.The excitation can be tuned to a specific wavelength adapted to the compoundunder study.

Two broad categories of commercial instruments are currently proposed bymanufacturers: fluorescence ratio fluorometers and spectrofluorometers.

Source

Emissionmonochromator

SampleExcitationmonochromator

Observation throughan acute angle or of 90°

IF

IF

Detector

Figure 11.7 A block diagram of a spectrofluorometer with a xenon arc lamp. The fluorescenceis measured, in contrast to studies on fluorescence dynamics, under ‘steady state’ conditions bymaintaining the primary excitation source. Below right, a schematic of a xenon arc lamp. Thepressure of xenon in the lamp is around 1 MPa. These arc lamps made from a quartz envelopeand without a filament, are sources of ‘white light’. The cathode is the finer of the two electrodes(reproduced courtesy of Oriel).


11.5.1 Fluorescence ratio fluorometers

The light emitted by the primary source initially passes through the excitationmonochromator which allows a narrow band of wavelengths to be selected (15 nm)to induce fluorescence of the molecules of interest in the sample solution. A part ofthe fluorescence emitted by the compound is collected in a direction either perpen-dicular or parallel (depending upon the model) to the direction of the incidentbeam. Then before the light reaches the detector it passes the emission monochro-mator allowing the selection of a narrow band of wavelength for measurement.Many manufacturers have commercialized models fitted with filters (Figure 11.8).These basic instruments contain a turret compartment for the standard solutions,the sample and a compound to be used as fluorescing standard. By alternating inthe same optical pathway (single beam models) the standard solutions, the samplesolution and a fluorescent standard reference (quinine sulfate, rhodamine B or 2-aminopyridine) the fluorescence ratios can be measured allowing to obtain, versusa calibration curve, the expected results. In this manner possible fluctuations fromthe source and a large number of regulatory parameters of the instrument areeradicated.

The use of a xenon flash lamp as the source enables the study of fluorescenceafter the source has been switched off. This method, used in immunology, in whichfluorescing lanthanide complexes are obtained having a fluorescencing lifetimeof around 1 ms, is sufficient for very sensitive measurements (in the picomolarconcentration range).

Source Detector

Excitationfilters (10 nm)

Emission filters (10 nm)

Optical fibres

Microwell

I0IF

96-wells microplate (0.5 mL)

405

460

510555

590

620355

444

485530

584

320

Figure 11.8 Schematic of the optical pathway of a fluorometer microwell-plate reader. A fibre-optic carries the excitation radiation to the wells chosen for analysis and a second fibre recoversthe fluorescence via a forward geometry. These fluorometers can read plates containing from 6up to 384 microwells, that is useful for routine control in combinatorial chemistry and otherimmunology/enzymology methods of screening.


11.5.2 Bench-top spectrofluorometers

Spectrofluorometers allow a more complete study of fluorescent compounds,notably by recording both excitation and emission spectra (Figures 11.9 and11.10). They comprise two grating monochromators, both of which are ableto scan a spectral band. It is possible to obtain the entire emission spectrumwhile maintaining a fixed excitation wavelength or to record the entire excitationspectrum while maintaining a constant emission wavelength.

Spectrofluorometers have software which can determine automatically theexcitation–emission pair to get the best results (Figure 11.10). Knowing the UV/Visspectrum of the compound, the procedure can be decomposed in the following steps:

1. The excitation monochromator is set to the value corresponding to themaximum of the UV absorption spectrum.

2. The fluorescence spectrum is recorded.

3. The emission monochromator is set to the wavelength of maximum fluo-rescence and the excitation wavelength is varied. The excitation spectrum isobtained allowing the best final choice of the excitation radiation (which canbe different from the UV absorption maximum).

It may be also useful to scan the excitation and emission monochromators simul-taneously (synchronous fluorimetry). Often, this is carried out by scanning the

Reference PMT

Grating

Grating

Excitationmonochromator


Horizontalslits

Detector PMT

Beamsplitter

150 Wattxenon lamp

Samplecuvette

Mobile shutter

Figure 11.9 Schematic of a Shimadzu F-4500 spectrofluorometer. A fraction of the incidentbeam, reflected by a semi-transparent mirror, reaches a reference PMT. A comparison of thesignals from the two PMTs leads to the elimination of any drifting of the source. This procedure,for single beam instruments, gives approximately the same stability as with a double beamspectrometer. However, the spectrum of a given solution will often present minor differenceswhen recorded upon different instruments (reproduced courtesy of Shimadzu).


500 600 700 800Wavelength (nm)

Fluorescence

Exc

itatio

n λ

440 480320 400360 200 240 320 360 400280

285 nm

240 nm

347 nm

280

0

20

40

60

80

100

0

20

40

60

80

100

nmnm

Rel

ativ

ein

tens

ity

Rel

ativ

ein

tens

ity

Emission spectrum Excitation spectrum

BA

o-diaminobenzene bis-hydrochloride C = 10 ppm in aqueous solution

NH2

NH2

2HCl

Figure 11.10 Fluorescence spectra. Above, emission–excitation matrix as a topographic repre-sentation in pseudo-3D of a mixture of two salts of uranium and terbium by varying thewavelength of excitation. This type of recording leads to the optimum conditions of measure-ment for such a mixture. Below, emission–excitation spectra. (A) Emission spectrum of fluores-cence obtained by maintaining the wavelength of excitation at 285 nm. (B) Excitation spectrumobtained by maintaining the emission monochromator at 347 nm during the recording.

excitation and emission monochromators at the same rate while keeping thewavelength difference (or offset) between them constant.

A fluorescence decay time is a measurement, at fixed wavelength, of fluorescencesignal as a function of time. Despite the fact that this time is very short, certaininstruments can measure the lifetime of fluorescence. There exist several methodsbased, either upon the recording of the decrease curve of the light intensity

11.6 APPLICATIONS 253

emitted when the excitation has ceased or, upon the comparison of fluorescencemodulation as a function of a rapid modulation of the excitation source.

11.6 Applications

Apart from about 10 per cent of all existing molecules that possess natural fluores-cence, many can be made fluoresce by chemical modification or by association witha fluorescent molecule. For example, a fluorophore reagent can be bonded to ananalyte by chemical reaction (the 7-hydroxycoumarins can be used to this effect).This is called fluorescence derivatization, reminiscent of the procedure employedin colorimetry.

For the determination of metal cations, chelates are created with oxine(8-hydroxyquinoline), alizarine or benzoin, then extracted by organic solvents.In biochemistry, fluorescence has numerous applications for the quantification ofproteins or nucleic acids by means of reagents which can affix with specificityto these compounds. This approach, sometimes very elaborate, in associationwith electrophoresis constitutes a more sensitive and less restricting method thandetection by radioactive substrates.

� Chemifluorescence (not to be confused with chemiluminescence) is equally aparticularly sensitive method for the detection of proteins. A specific antibody of thisprotein is required for this which is bound to a conjugated enzyme, such as a phos-phatase (Figure 11.11). If mixed with a substrate such as a phosphate derivative offluorescein, the latter is released then revealed by its fluorescence which is provokedby a suitable source of excitation.

Excitation at 532 nm

Cleavage

Emission at 550–570 nm

Fluorescein

Phosphate group

Substrate“Fluorescein-phosphate”

Phosphatase

Conjugated antibody

Protein

Figure 11.11 Procedure of protein measurement by chemifluorescence in biochemistry. Thediagram gathers together the reaction sequence concerned, knowing that to undertake such ameasurement a protocol, in which the different reactions are considered as distinct steps, mustbe followed.


To improve analyses by HPLC, amines can be fluorescently labelled renderingvery low thresholds of concentration detectable, in the order of attomoles�10−18 M�.

Amongst the classic current applications of fluorescence are measurements ofpolycyclic aromatic hydrocarbons (PAH) in drinking water by HPLC. In thiscase the detector is equipped with a fluorescence flow cell installed at the outletof the column. This mode of detection is particularly well adapted for attainingthe threshold norms imposed by legislation. The same process can be adoptedfor measuring the aflatoxins (Figure 11.12), as well as numerous other organiccompounds such as adrenalin, quinine, steroids and vitamins.

H

H

H

H

UV detection at 365 nm

796-

0028

, 002

9

Chemical structures of aflatoxins B & G

Conditions :RP-18 Column, 25 cm, 5 μm particlesMobile phase: water, acetonitrile, methanol(60 : 20 : 20)Injection of a mixture of 4 aflatoxins:

0 5 10 min

0 5 10 min

Aflatoxin B1 Aflatoxin G1

Note:Aflatoxins B2 and G2 do not possessa double bond in the left hand ring

OMeOMeO

O

O

O

OO

O

O O O

O

1

2

3

4

MirrorPMT


Cell

Lenses

Photodiodes

Xenon arc lamp

Excitationmonochromator

Fluorometricdetectionat 440 nm(excit at. 360 nm)

1 - Aflat. G2 (0.3 mg/L)2 - Aflat. G1 (1 m g/L)1 - Aflat. B2 (0.3 mg/L)2 - Aflat. B1 (1mg/L)

Figure 11.12 Comparison, following a chromatographic separation, of UV and fluorescencedetection. Aflatoxins, which are carcinogenic contaminants present in certain batches of graincereals, are the subject of analysis by HPLC. Detection by fluorescence is much more sensitiveto G2 and B2 than with UV detection (reproduced courtesy of SUPELCO). Below left, schematicof the different components of a LC-detector based upon fluorescence. This detector is ableto find rapidely, for each compound eluted, the best coupling of excitation/emission withoutinterrupting the chromatography underway (reproduced courtesy of a document from AgilentTechnologies).

11.7 TIME-RESOLVED FLUORIMETRY 255

11.7 Time-resolved fluorimetry

This time-resolved fluorescence technique allows a measure of the time depen-dence of fluorescence intensity after a short excitation pulse. It consists of obtaininga spectrum measured within a narrow time window during the decay of thefluorescence of interest. The usefulness of this technique is now well proven forbiochemical assays and immunoassays. Lanthanide chelates have luminescencedecay times over 600 s, which allows time-gated fluorecence detection, with acomplete rejection of other fluorecence signals. For these quantitative applications,the primary source is generally a quartz lamp associated with a splitter.

There are several ways to perform time-resolved fluorescence measurements.Since the time dependence of fluorescence emission is typically on a picosecondto nanosecond time scale it is very difficult to achieve. To overcome this difficultyeither a frequency domain method or the single photon counting approach is used.

For studying fluorescent compounds per se, lifetime spectrometers are used.A highly diluted solution of the compound to be studied is submitted to a pulsedsource (laser diode for example) repeatedly for several picoseconds, at frequenciesof several megahertz. During these successive cycles, when the source is switchedoff, the detector measures the time until a photon of fluorescence reaches it. Thenthis event is stocked in the memory channel reserved for the corresponding time.After having accumulated a large number of photons, the graph of the decay is

cycle # 1

cycle # 3cycle # 2

cycle #n

Detector response

Time (ns)

Excitation flash

0 10 30 4020

Fluorescein 1x10-9M

Histogram (t)

Time

Int.

(CP

S)

Int.(

CP

S)

• • •

• • •

Figure 11.13 Representation of fluorescence decay and of the principle of the measurement.On the graph, each point represents the contents of a memory channel (coupling time/numberof photons). The exponential curve of decay appears here in the form of a straight line. This isdue to the choice of a logarithmic scale for the ordinate. On the right, a representation of theTCSPC (time-correlated single-photon counting).


finally constructed by creating a histogram of the contents of all of the memorychannels (Figure 11.13).

11.8 Chemiluminescence

Chemiluminescence is a particular form of phosphorescence. The excited molecules,which leads to phosphorescence, are produced during a chemical reaction. In theexample of Figure 11.14, fluorine acts as a strong oxidizing agent when trans-forming the dimethyl sulfide. A portion of the energy liberated by this reaction isemitted in the form of light.

� Luminol and diphenyl oxalate are two compounds very frequently used in a varietyof classic applications from non-electric emergency lighting to the hoops, necklacesand light batons sold at fairgrounds. The reactions that causes emission are alloxidations by hydrogen peroxide.

These reactions make available numerous measurements of great sensitivity. Ifthe use of luminol to measure ferrous iron or hydrogen peroxide is anecdotal,

breaking down

Dye*

emissionphotons

H3C-S-CH3 + F2 products + photons

products + photons

+

+

PhO

O

OPh

OO O

OO

+ 2PhOH

NH

NH

NH2 O

O

2 CO2

Fe++

Diphenyl oxalate

Luminol

H2O2

H2O2

Dye

Figure 11.14 Examples of chemiluminescence reactions. The nature of the reaction products issometimes not well known. Luminol emits an intense ‘electric blue’ light while the diphenyloxalate, depending upon the colouring agent used, leads to the emission of a great variety ofcolours.

11.8 CHEMILUMINESCENCE 257

there exists a certain number of significant applications for chemiluminescence inchemical analysis, such as those which make use of ozone as an oxidizing agent.

This strong oxidizing agent enables the measurement of nitrogen monoxide(oxidized to nitrogen dioxide) with the aid of an automatic instrument thatincludes an ozone generator (Figure 11.15). The field of application for thismeasurement is broader than it might seem, ranging from studies of pollutedatmospheres to the measurement of the total quantity of nitrogen in an organicsample – on condition that the nitrogen has undergone a previous transformationby combustion to nitrogen dioxide – as the quantitative transformation of nitrogendioxide to nitrogen monoxide provides the basis for the measurement.

Inversely, ozone can in its turn be measured by chemiluminescence in thepresence of ethylene (Figure 11.15).

The same principle can be applied to measuring sulfur first transformed tosulfur dioxide �SO2� by combustion in the presence of oxygen (Figure 11.16),then reduced to hydrogen sulfide �H2S� before being finally re-oxidized by ozone(with chemiluminescence).

In gas chromatography some detectors, selective for the elements S and N, usethis sequence of reactions (Figure 11.17).

Luminol, whose chemiluminescence in the presence of hydrogen peroxide, canreadily be catalysed by horseradish peroxidase (HRP), has found an applicationin the calibration tests for enzyme-linked immunosorbent assay (cf. Section 17.7).The intensity of the emission, is stable during a few minutes, what makes thismethod extremely sensitive over an extended range of concentrations, which isunusual for this kind of test.

Chemiluminescence is used in enzymology. With a specific enzyme, somespecially prepared reagents liberate unstable intermediates whose decomposition

Sample containing nitrogen

Drying

Pure oxygenAnalytical

results

Detector(PMT)

hνNONO

O2

O3

O2NO2

O2

Towards vacuum

Reactor

Combustionat 1100 °C

Ozonegenerator

–O2

NOO3

NO2* NO2 + photons

Sensitivity: 1 ppb < CNO < 20%

Figure 11.15 Functioning principle of an analyser based upon nitrogen monoxide lumines-cence. This apparatus is able to find all compounds containing nitrogen by a specific emis-sion of light. Installed at the outlet of a GC column, the instrument becomes a selectivedetector.


*

O3Ethylene

+ photonsH2C

O

CH2 H2C

O

CH2

+ photons

+ various....

+ various...H2S

H2

O2

O3

SO2

SO2

SO2*

(Sulphur compound)

–H2O

Figure 11.16 Reactions of chemiluminescence using ozone. The scheme above summarizes theprinciple of transformation of a sulfur compound oxidized to sulfur dioxide in the excited stateby ozone. Below, the final reaction can be applied to the measurement of ozone just as readilyas for ethylene.

Figure 11.17 Analyser of sulfur and nitrogen. Model 9000NS reproduced courtesy of Antek.This instrument combines two luminescence techniques: nitrogen is measured by chemilumi-nescence of NO (see Figure 11.15) while the sulfur is measured by fluorescence of SO2 (UVexcitation).

PROBLEMS 259

is accompanied by the emission of light. The alkaline phosphatases or the beta-galactosidases are quantified with precision by this procedure.

Problems

11.1 Calculate the position of the radiation of Raman diffusion for a monochro-mator of excitation regulated to 400 nm; the solvent used is cyclohexane.(Recall that for cyclohexane, the Raman diffusion corresponds to a radiationdisplaced by 2880 cm−1 with respect to the wavelength of excitation.)

11.2 A test for the sensitivity of a fluorometer is to measure the intensity offluorescence of the Raman diffusion peak of a cell filled with water and withan optical pathlength of 1 cm. If the wavelength of excitation is regulated to250 nm, at which wavelength must the measurement be made (the Ramandisplacement of water is 3380 cm−1)?

11.3 An unknown aqueous solution of 9-aminoacridine in water leads to anintensity of fluorescence which, measured at 456 nm, is of 60% with respectto an external reference. A standard solution of this compound, the concen-tration of which is 0.1 ppm in the same solvent, leads to a fluorescence of40%, under the same conditions. Water alone, equally under the conditionsof the experiment, presents a negligible fluorescence.

1. Calculate the ppb concentration of 9-aminoacridine in the unknownsample.

2. For quantitative analysis, how can one avoid confusing the Ramandiffusion and the fluorescence of the compound?

11.4 3,4-benzopyrene is a dangerous aromatic hydrocarbon frequently present inpolluted air, measurable in a solution of dilute sulphuric acid, by fluorimetry.The excitation wavelength is 520 nm and the measurement taken at 548 nm.

10L of contaminated air is bubbled in 10 mL of sulphuric acid. Thefluorescence of 1 mL of this solution measured at 548 nm is 33.33 (arbitraryunits). Two standard solutions, one containing 0.75 mg and the other1.25 mg of 3,4-benzopyrene per mL of the same diluted sulphuric acid,led for extractions of 1 mL to values of 24.5 and 38.6 (same unit scale).A sample not containing the 3,4-benzopyrene was recorded as 3.5 (sameunit scale) by the fluorometer under the same conditions.


1. Explain why benzopyrene is fluorescent.

2. Calculate the mass of 3,4-benzopyrene per litre of air.

3. Express the result of this measurement in ppm.

11.5 Ferrous iron catalyses the oxidation of luminol (see below) by hydrogenperoxide. The intensity of the chemiluminescence which follows increaseslinearly with the concentration of Fe(II) as it rises from 10−10 M to 10−8 M.To measure a solution of unknown content in Fe(II), 2 mL of the solu-tion was extracted and then introduced to 1 mL of water, followed by theaddition of 2 mL of hydrogen peroxide and finally 1 mL of an alkali solu-tion of luminol. The luminescence signal is emitted and integrated over aperiod of 10 seconds giving a value of 16.1 (arbitrary units). In a secondattempt, 2 mL of the unknown Fe(II) solution is again extracted and onthis occasion it was added to 1 mL of a solution 515 × 10−5 M in Fe(II)and the same quantities of hydrogen peroxide and luminol were intro-duced as before. The signal, integrated over 10 seconds, was measuredas 29.6.

Calculate the molar concentration of Fe(II) in the original solution.

11.6 For the determination of the zinc concentration in an unknown solutionA, by the method of standard addition, a standard solution B is preparedwhose pure zinc chloride concentration is 0.1 mmol/L �M = 1362g/mol,Zn = 6538�. 5.0 mL aliquots of the unknown solution A were introducedinto four separatory funnels. 4.0 mL, 8.0 mL and 12.0 mL portions of thestandard solution B were added to three funnels. After stirring and extracting(three times), with 5.0 mL of tetrachloromethane containing an excess of8-hydroxyquinoline, the extracts were diluted to 25 mL. The following fluo-rescence readings were obtained:

PROBLEMS 261

mL of the solution B added Fluorescence reading

0 7654 13958 196

12 258

1. Explain why the extraction with CCl4 is performed in the presenceof hydroxyquinoline.

2. From the data in the table and by the method of least squares derivean equation for the calibration curve.

3. Calculate the ppm concentration of zinc in the unknown solution A.

11.7 Fluorimetry is the method selected to measure the concentration of quininein a commercially available drink. The excitation wavelength is 350 nm andthe wavelength for taking the measurements is 450 nm. From solution A,of quinine, at 0.1 mg/L, a series of standards is prepared to establish acalibration curve.

Solution Volume of A Fluorescence (arb. units) H2SO4005M

Standard 1 20 182 0Standard 2 16 1388 4Standard 3 12 1092 8Standard 4 8 758 12Standard 5 4 395 16Blank 0 0 20

An extraction of 0.1 mL is taken from the original solution which is thendiluted to 100 mL with H2SO4�005M. The value for the signal of thissolution is 113.

1. Using least squares, equation from these data calculate the calibration.

2. What is the concentration weight/volume (w/v) of quinine (g/L), andin ppm?

3. Why in quantitative analysis is it preferred to take measurementsusing a fluorometer rather than with a spectrofluorometer?

12X-ray fluorescence spectrometry

X-ray fluorescence is an atomic spectral property, universally recognized as a veryaccurate method currently exploited under this same name to provide qualitativeand quantitative information on the elemental composition of all types of samples.The principle of operation involves irradiating the sample either with an X-raybeam or by bombardment with particles, such as electrons having sufficient energy,in order to observe the resulting X-ray fluorescence (XRF) emitted by the sample.The universal character of this phenomenon as well as the possibility to rapidlyexamine samples, most often without preparation, explains largely the success ofthis non-destructive analytical method. The technique encompasses a wide varietyof instruments, ranging in size from portable analysers for instant analyses tohigh-resolution spectrometers, including X-ray probes fitted to scanning electronmicroscopes to make specified analyses or a mapping of the elements present.

12.1 Basic principles

When a sample, used as the target, is irradiated with a source of photons orbombarded with particles of high energy (between 5 and 100 keV), a X-ray fluo-rescence is most often observed (Figure 12.1). The spectrum of this photolu-minescence is made up of radiations with wavelengths and intensities that arecharacteristic to the atoms present in the sample.

The modes of excitation which can provoke X-ray fluorescence are various:photons or particles such fast electrons, protons, � radiation. Whatever the methodchosen, the X-ray emission yields nevertheless an identical spectrum.

The emission spectrum depends very slightly on the chemical combination orchemical state of the elements in the sample. For this reason, this non-destructivemode of analysis can be used for all elements starting from boron �Z = 5� touranium �Z = 92� in solid or liquid homogeneous samples, without, theoretically,any fastidious preparation.

Although semi-quantitative analysis does no present any major difficulty, quan-titative analysis is not quite simple, because a significant part of the emittedradiation from the outer surface of the sample is re-absorbed before being able


264 CHAPTER 12 – X-RAY FLUORESCENCE SPECTROMETRY

X-rays generator

Wavelength dispersivespectrometry (WDXRF)

Mobile or fixed detector(s)

CrystalCollimator

Sample

Detector(s)

PrimaryX-rays

SecondaryX-rays

Energy dispersivespectrometry (EDXRF)

Detector sensitive toX-photon energy

1 2

Figure 12.1 X-ray fluorescence. The sample when excited by a primary source of X-rays emitsa fluorescence radiation which can lead to two representation of spectra depending on thedetector: (1) Energy dispersive spectrum (ED-XRF) obtained by means of a cooled diode thatgives a signal according to the energy of each incident photon: (2) Wavelength dispersivespectrum (WD-XRF) obtained through use of a rotating crystal functioning as a grating. Thisgoniometric assembly contains one or several mobile detector(s). However, since energy andwavelength are linked (expression 12.2), the spectra are presented in units of energy (eV),whatever the mode of detection.

to escape from the sample. So far the influence of the matrix is clearly taken intoaccount, especially when the sample is not homogeneous, the results can be asprecise as those obtained by atomic absorption or emission.

In general, X-ray fluorescence spectrometers consist of a source of excitationradiation, a radiation detector to detect the stimulated radiation from the sampleand a display of the spectral output. Since each element has a different andidentifiable X-ray signature, the presence and concentration of the element(s)within the sample can be determined.

12.2 The X-ray fluorescence spectrum

X-ray fluorescence of an isolated atom results from a two-step process.The first step is the photo-ionization of the atom. The energy of the incident

photon is transferred to an innermost electron (a K electron) which results in theejection of this electron of the atom, named a photoelectron, assuming that thephoton has sufficient energy. This photoelectric effect leads to an ionized atom asa consequence of the missing electron (Figure 12.2).

� The excitation energy produced is sometimes transferred to one of the outerelectrons, causing it to be ejected from the atom. This is an ‘Auger electron’. Theenergy of each photoelectron is equal to the difference between the energy of theincident X-ray photon and that of the energy level initially occupied by the ejected

12.2 THE X-RAY FLUORESCENCE SPECTRUM 265

E

K

LMN

Ionisationhν

hνhν1

hν1

hν2

hν2

hν3

hν3 hν4

hν5

hν4

hν5

K

L

M

N

incoming primaryX-ray radiation

Prim

ary

X-r

ay

e–

e–

Kα

Kβ

LβLα

Lα

MαKα Kβ

LβMα

Photoelectron

K transitionsL transitions

M transition

an Augerelectron

Figure 12.2 Schematic of the X-ray fluorescence process. For this classic image of a medium-sizeatom are displayed different possible electronic reorganizations when an electron in the K shell isejected from the atom by an external primary excitation X-ray, creating a vacancy. The differentK, L and M transitions are not significantly affected by the nature of the chemical combinationin which the atom is found. In this way the sulphur line K�1 changes from 0.5348 nm for S6+

to 0.5350 nm for S0. This difference of around 1 eV is comparable to the natural linewidth forX-ray radiation.

electron. The photoelectron energy spectrum is the basis of a method called ESCA(electron spectroscopy for chemical analysis).

The second step is the stabilization of the ionized atom. It corresponds to there-emission of all, or part, of the energy acquired during excitation. Almostinstantaneous (in 10−16 s), an electron from an outer orbit of the atom ‘jumps in’to occupy the vacancy. Since outer shell electrons are more energetic than innershell electrons, the relocated electron has an excess of energy that is expended asan X-ray fluorescence photon. In this way, the atom returns to its ground statevery quickly.

Cascade electronic rearrangements are observed for heavy atoms, in contrast tolighter elements whose electrons are distributed over a smaller number of groundstates.

This reorganization produces photons of fluorescence. If E1 is the energy of theinitial electron and E2 the energy of the electron which comes to fill the createdhole, a radiative transition (‘a fluorescent photon’) will occur, with a probabilitybetween 0 and 1, and characterized by a frequency �, such that:

h� = �E2 − E1� (12.1)

The interpretation given above is simplified since fluorescence is not the onlyprocess by which the atom can lose its excess energy. When a primary X-raystrikes a sample, it can be absorbed or scattered through the material. Otherphenomena occur such as Rayleigh scattering (elastic scattering) and the Comptoneffect (inelastic scattering with release of Compton electrons).


Each atom, from Z = 3, leads to a collection of specific radiation, obeying thequantum selection rules of its electrons ��n> 0��I =±1�. Hydrogen and heliumdo not have X-ray fluorescence spectra since they do not possess an electron atlevel L. From beryllium to fluorine a single transition of type K� is noted. Thenas the atoms become heavier the number of possible transitions increases (75 formercury) though the probability of some of them are very small. Fortunately, onlya few intense transitions are required to characterize an element (five or six atmost).

For all elements, fluorescence appears in the broad energy range from 40 eVto more than 100 keV (wavelengths from 31 to 0.012 nm, as calculated fromexpression 12.2).

The precise designation of the possible electronic transitions depends upon theorbital energy levels of the atom under study, for which a simplified nomenclaturedue to Siegbahn is used. For example, for the element iron, FeK�2 refers to atransition corresponding to the transfer of an electron to the level K, comingfrom the neighbouring level M; � indicates the transfer M-K and 2 the intensityrelative to the strongest transition in the series (1 being more intense than 2). TheK� transitions are approximately six times less likely to occur (thus less intense)than the corresponding K� transitions (� marking the shortest ‘distance’). Forthe levels multiple L and M, the notation according to Siegbahn is not alwayssufficiently explicit.

Taking account of the expression E = hc/ linking the energy of a photon toits wavelength , the radiation emitted can be equally characterized by either itswavelength (nm or angströms) or by its energy E (eV or keV). The two mostcommonly used expressions of conversion are:

�nm� = 1240

E�eV�

or �nm� = 124

E�keV�

or Å = 124

E�keV�

(12.2)

12.3 Excitation modes of elements in X-ray fluorescence

To induce X-ray fluorescence of elements in a sample, a source of photons orparticles of sufficient energy is required. Generally these sources are producedby X-ray tubes of variable power or, for portable instruments, by radioisotopicsources. If the term of X-ray fluorescence is considered in the broadest sense ofX-ray emission, other excitation processes employing particles (e−, �) can be used.

12.3.1 X-ray generators

In an enclosed space maintained under vacuum a beam of electrons, acceleratedthrough a PD of up to 100 kV, hits a target serving as the anode (called anticathode),

12.3 EXCITATION MODES OF ELEMENTS IN X-RAY FLUORESCENCE 267

–

-–+–

+

Continuous spectrumI0

Wavelength (nm)

Rhodium (45Rh) anticathodewith a potential drop of 62 kV

Characteristicspectral lines

Kα

Kβ LαLβInte

nsity

(C

ps)

X-ray’s beam

Beryllium windowAnticathode

High vacuum

Circular filament(cathode)

High Volt. Water coolingElectricalsupply

(filament source)

0.055

0,0615

0,46 nm

0,44

0.02

e–

K lines L lines

Figure 12.3 X-ray emission spectrum produced by impact of electrons on a target anode anddetails of an X-ray tube. The line spectrum from the anode can be observed as a superpositionon the continuous part of the radiation, which depends upon the potential difference applied.A continuum spectrum is needed for applications requiring high penetration power, such asradiology. These lines after being isolated by means of filters, are used as monochromaticsources. Water cooling is compulsory if the X-ray tube operates at high power (1–4 kW), whilenot necessary for tubes of routine apparatus generating a few watts. To make monochromaticsources (without continuum spectrum), an adapted monochromator or a tube of this typeis used to excite a second target of which the fluorescence relays the first, this time withoutbremsstrahlung radiation.

which is made of a metal with an atomic number between 25 and 75. Thisbecomes the source of primary X-rays. The emission corresponds to a continuumspectrum (white bremsstrahlung radiation), due to the slowing down of electronsin the target, and of the very intense fluorescence lines whose wavelengths arecharacteristic of the metal that constitutes the anode (Figure 12.3). The wavelengthend point 0 of this spectrum, which depends upon the PD, can be calculatedby expression 12.2. In order to have high-energy spectral lines, useful for certainapplications, metals with a high atomic number are chosen for the X-ray tubetarget: rhodium (K� line at =0061nm; E =203keV), tungsten (K� line at =0021nm; E = 59keV), gadolinium, etc. Nowadays, X-ray detectors are extremelysensitive and consequently the power demanded from the generators tends to bereduced.

� An X-ray generator itself constitutes an application of X-ray fluorescence and itis not surprising therefore that in the past spectrometers were conceived using thesample as the anticathode, on condition that it conducts electric current. The powerrequired to induce fluorescence through a mechanism involving electrons is lowerthan that required by the impact of photons.

For portable instruments (Figure 12.4), miniature X-ray generators of low power�<500mW� have been developed. The required electrons that produce X-rays ina target material (Cu) are obtained either by impact laser or from a pyroelectriccrystal.


Figure 12.4 Miniature size X-ray generator and detector. These probes are used with portableapparatus though their control modules or power units are nevertheless more bulky (reproducedcourtesy of Amptek Inc.).

Temperature +V Earth

8-8.2 keV

Emission spectrum of an heating/cooling cycle

9 keV

3 min

Time

Cooling (Cu X-rays)

Heating(Ta X-Rays)

X-r

ays

Inte

nsity

X-r

ays

Inte

nsity

Low PressureGas e(–)TemperatureSensor Heating/cooling

Pyroelectriccrystal

Copper target

Beryllium windowX-rays

Figure 12.5 Low-power X-ray generator. Reserved principally for portable instruments becauseof their smaller volume (diam. 15 mm). The production of Cu X-rays on the diagramcorresponds to the cooling time. The heating/cooling cycle is about 3 min. When the crystaltemperature reaches its low point, the heating phase starts again. The above are characteristicsof the model Amptek COOL-X.

The generator taken as an example (Figure 12.5) uses a pyroelectric crystal(tantalum) oriented in a fashion so that its top surface depolarizes reversibly whenheated. In this way, when the temperature increases the uppermost face gets posi-tively charged and attracts electrons from the ionized gas in the surroundings. White

12.3 EXCITATION MODES OF ELEMENTS IN X-RAY FLUORESCENCE 269

radiation appears (bremsstrahlung X-rays) as well as fluorescent lines of tantalum (L�of 73La). On cooling, the upper face of the crystal becomes negative. The electronsthen are accelerated towards a copper target, which is at the ground potential. At thispart of the cycle, the radiation contains the spectral lines of this element as well asbremsstrahlung X-rays. The cycle time can be varied from 2 to 5 min.

12.3.2 Radio-isotope sources of X-rays

Besides the generators described above there are X-ray sources based on radioactivematerials to provide the excitation of the sample. The advantage of using thesematerials is that an isotope can be selected to provide a mono-energetic beam ofradiation that is optimized for the specific application. One method consists toselect a radionuclide that is transformed by internal electron capture (IEC). Thismode of decomposition corresponds to the transition of one level-K electron intothe nucleus of the atom. For a nuclide X, the phenomenon is summarized asfollows:

AZX

IEC−−−→ AZ−1Y

∗ h�−−−→ AZ−1Y

The missing electron is quickly replaced by an other electron coming from anouter shell accompanied with emission of a photon of X-ray fluorescence fromthe resulting nucleus (Figure 12.6).

There are several known radionuclides of this type, including 109Cd, 57Co, 55Fe,which have sufficiently long periods, that they can be used as different energysources (Table 12.1). The activity of these isotopic sources is generally of severalmCi, generating a flux of 106 to 108 photons/s/steradian. Of small size they areusually reserved for portable instruments. The isotope or combination of isotopesused for any application is selected based on the ability of the selected isotope(s) to

4 7 keV

5,9

CP

S

150 eV

6,46,4 keV

5,9 keV

K K

L L

M25Mn55

M

transformation of 55Fe into 55Mn(partial configuration)

nucleuselectron

e–

or

Kα

Kβ

26Fe∗55

65

Figure 12.6 Radioactive source 55Fe. Emission spectrum obtained by placing a 55Fe sourcein the sample compartment of an energy dispersive spectrometer. The signal corresponds tothe X-ray fluorescence of 55Mn, that is the nucleus arising from 55Fe decomposition. On thisspectrum, the resolution at 5.9 keV, measured at mid-height (FWHM) is around 150 eV.


induce fluorescence of the element being measured. However, these sources requirea permit for using, and can pose problems of transport, storage, or maintenanceas they emit continuously unlike more classic generators.

A �− emitting radionuclide may also be associated with a second element to beused as a target which functions as the anode of a conventional X-rays tube. Forexample, the association 147Pm/Al (� = 26 years) emits a continuous X-ray decel-erating radiation between 12 keV to 45 keV. The chief drawback of the methodis the need for periodic source replacements to compensate for source decay.

Table 12.1 Several radio-isotopic X-ray sources

Transition Half-life (years) X-ray (nm) E (keV)

55Fe → 55Mn 27 MnK� 021 5957Co → 57Fe 07 FeK� 019 64109Cd → 109Ag 13 AgK� 0056 220

12.3.3 Other sources of excitation

� Emitters

To generate X-rays, � radionuclide such as americium 244Am (� = 430 years) orcurium 244Cm can also be used. During the � collisions, internal electrons areejected, in turn exciting the X-ray fluorescence of the target. The intensity is ofseveral tens of mCi. This source also produces � radiation of 60 keV.

� The Martian probes launched in 1996 and during the summer of 2003 by the JetPropulsion Laboratory were carrying small robotized vehicles, each one containing aAPXS (alpha particle X-ray spectrometer) whose source contains 244Cm(30 mCi). Themodules are mounted upon a telescopic arm in order to gain a sufficient proximity tothe rocks to be able to analyse. This radioisotope provokes a nuclear reaction of type�� with light elements, causing the appearance of protons of energy characteristicto the element, while for heavier elements the X-ray fluorescence yields informationupon the identity of the elements present. To improve the resolution of the detectors,which are semi-conductors (cf. section 12.4), the X-ray fluorescence spectra arerecorded during the night, which provides the apparatus with a cooler and stableambient temperature.

AZX + 4

2He −→ A+3Z+1Y

∗ + 11H

Fast electrons

X-ray fluorescence emission can be induced by electrons and therefore it is notsurprising that chemical analysis can be performed using electron microscopes

12.4 DETECTION OF X-RAYS 271

Primary electrons

Sample surface

Secondary electrons

Absorbed electrons

Secondary X-ray fluorescence

ContinuousX-ray emission

CharacteristicX-ray emission

Back-scattered electronsX-rays

(0.2 − 2 µm)

Figure 12.7 ‘Pear’-shaped interaction of the electron beam with the material. Differentphenomena are produced in a small volume beneath the surface of the material. A complexemission results in which the origins of a collection of different radiation can be determined. Ifthe energy is appreciably high, then the X-rays are formed at a greater depth within the materialand consequently it will be more difficult to detect them.

(SEM). When the object is ‘illuminated’ by highly energetic electrons, which arenecessary to generate SEM images, diverse interactions are produced within asmall pear-shaped volume surrounding the impact zone (Figure 12.7). An X-rayemission characteristic of the atom composition of that zone being subjected tothe electron bombardment is observed. In this case, the sample plays the role ofthe anode in an X-ray tube. This is why many electron microscopes are equippedwith an accessory that can collect a fraction of the X-ray fluorescence to do theanalysis of the observed sample. The energy of the electron beam is adjusted tobetween 20 to 30 keV, for which there is a compromise to allow the appearanceof K or L spectral lines, leading to characterization of most elements. This quasi-instantaneous analysis, called X-ray microanalysis, relates to a sample volume ofapproximately 1�m3.

12.4 Detection of X-rays

X-ray detectors are transducers that count individual photons. In a photoelectricinteraction, the entire incident energy of the interacting photon is stored up inthe detector (while in Compton scattering, only a portion of the incident energyis deposited). The detector works with greater accuracy, as the photon flux isweaker. The two most current types are:

• The gas transducer working as a proportional counter. Each X-ray photonprovokes an ionization in a gas mixture (e.g. argon/methane) which gives apulse proportional to its energy (Figure 12.8).


–

Hole

U

Active zone

FET

e–

X-rays

–200 V

P type region

N type regionBerylliumwindow

Diode

X-raysX-rays

+

–

(a) (b) (c)

filling gas

Int. UMounting stud

Cooling(by Peltier effect)

FET +

Figure 12.8 The two categories of detectors used for energy dispersive X-ray fluorescence spec-trometry. (a) Proportional counter used in pulse mode; (b) Cooled Si/Li diode detector usingPeltier effect (XR detector by Amptek Inc.); (c) Functioning principle of a scintillation detectorcontaining a large size reverse polarized semi-conductor crystal. Each incident photon generatesa variable number of electron-hole pairs. The very high quantum yield enables the use of lowpower primary sources of X-rays (a few watts or radio-isotopic sources).

• The semi-conductor transducer (scintillation counter). Each X-ray photonincreases the conductivity of the active zone (the junction) of a lithium-doped silicon diode (one electron for around 3.6 eV). The background noiseis reduced if the sensor is maintained at low temperature (cooled by liquidnitrogen or a Peltier device). The entry surface is protected by a berylliumfilm of a few �m (transparent for Z>11) (Figure 12.8). In one or other casesthe impulse furnished by the detector allows to go back to the energy of theincident photon.

To classify the photons with better precision their amount is limited to approx-imately 10 000/s by reducing, if necessary, the source intensity. The instrument’sdata system should accurately identify the energy of the photons, which arrive asa pack. The resolution of these instruments is given by the width at half-heightof the K� line of manganese, emitted by a 55Fe radioactive source (Figure 12.6).Energy dispersive instruments have a resolution around 100 eV, a much greatervalue than the natural width of the spectral lines.

After having defined a range of acquisition from between 10 to 20 eV, the multi-channel analyser (with, for example, a few thousands channels) will count thepulses caused by photons received during the several minutes of the measurement.Each photon will be classified in an energy channel corresponding to an interval ofseveral electron volts. The resulting spectrum is a histogram (Figure 12.6). Thesedetectors undertake simultaneous analyses over the whole spectral range, whichwill be better if the acquisition of signals is made during a longer period of timet (the sensitivity increases as

√t). Energy calibration is often performed using an

external reference such as cobalt K� transition.

12.5 DIFFERENT TYPES OF INSTRUMENTS 273

12.5 Different types of instruments

X-ray fluorescence spectrometers are classified into two categories depending howthe spectrum is obtained: the classic procedure of analysing wavelengths (‘WD-XRF’) or the alternative methodology of analysing the energy of the photonsemitted by the sample (‘ED-XRF’) (Figure 12.9). To the first category belongsa particular group of instruments fitted with filters (monochannel type) anddesignated for highly specific measurements.

12.5.1 Energy dispersive X-ray fluorescence instruments (EDXRF)

Energy dispersive instruments of small dimensions are reserved for both qualitativeanalysis and routine measurements (Figures 12.10 and 12.11). The spectrum isobtained by use of a detector installed quite close to the sample, which distinguishesthe energy of each of the fluorescence photons captured. These instruments areequipped with either a small size and low power X-ray tube (around 10 W) or aradioactive source for field instruments.

12.5.2 Wavelength dispersive X-ray fluorescence (WDXRF)spectrometers

In this second class of spectrometers, known for their excellent spectral resolution,the X-ray radiation emitted by the sample passes through a collimator made of long

... ......

X-ray sourceor electrons

Sample

X-RF

XRF

XRF

Sequential analysis

Multichannel systems

Single channel systems

Simultaneous analysisEnergydetector

12.5.1

12.5.2

12.5.2

Rotatingcrystal

Crystal 2

Crystal 1

Crystal n...

Detector 1

Detector 2

Detector 3

Goniometer

Set of pairedfilters

Detector(GM)

Measure element 1

Measure element 2

Measure element n

Measurementof a single element

“2 théta”

keV

Figure 12.9 Several approaches for obtaining spectra or X-ray fluorescence. On the figure areindicated the paragraph numbers in the text.


X-ray of a St Gaudens gold coin

109Cd excitationsource

Composition:90% Au10% Cu

Au M

Energy (keV)0 2 4 6 8 10 12 14 16 18 20 22 24

Au-L

Cu-k

Figure 12.10 EDXRF. Spectrometer containing a low power X-ray tube, as an example ofnumerous models of this type (model EX-310S reproduced courtesy of Jordan Valley). A typicalspectrum obtained with such an instrument (reproduced courtesy of Amptek Inc. USA).

Sample carousel

Filters

X-ray tubeAmpli.

High voltageEnergy Dispersivespectrum PIN diode detector

Multichannelanalyzer

Figure 12.11 Organization of the different sections of an X-ray fluorescence energy dispersiveinstrument, taking as example the MiniPal by Philips Analytical.

metal wafers (Soller slits), before hitting a crystal which is cut in such a way thatits constitutive atoms form planes parallel to the surface (Figures 12.1 and 12.13).These planes, separated between them by a distance d, behave like a stack of parallelmirrors when the angle of incidence � is the same as the angle of observation of thereflected light (Figure 12.12). The combination of these mirrors has the same effectas a grating: the only radiation observed will be that for which the wavelengthsatisfies the Bragg relationship (n being a whole number called the order ofdiffraction).

n = 2d sin � (12.3)

For construction reasons, � can vary from 5 to about 80 �. A greater value of dleads to greater wavelengths, however the resolution of the instrument is linked to

12.5 DIFFERENT TYPES OF INSTRUMENTS 275

θ

θ

θ

θ1

2

1

2

3

d

d

2

1Crystal Plane (Miller indices) d(Å)

TopazeLithium fluorideSiliconGraphiteOxalic acidMicaLead stearate

303200111001001002

1.3562.013.146.695.859.9651

Figure 12.12 Reflecting crystals used in goniometers of wavelength dispersive spectrometers andthe Bragg relationship. For the two beams 1 and 2 to be in phase, the difference in theiroptical path must be a multiple of . When this condition is met for the planes 1 and2, it will be simultaneously for all of the other planes and the global effect will thereforebe reinforced. This is the principle of constructive interference. Each crystal may be suit-able for a range of wavelengths. The broader this range is searched, the greater the inter-reticular distance must be for the crystal chosen, though the smaller will be its angulardispersion.

the power of dispersion d�/d, which is calculated by differentiating expression12.3 and which is inversely proportional to d:

d�

d= n

2d cos�(12.4)

These instruments can be classified as:

• Sequential analysers. These instruments are reserved for non-routine elementalmeasurements. The detector and the crystal undergo simultaneous andsynchronized rotations to ensure the detection of � and 2�, to a precision of1/1000 degree of an angle (Figure 12.13).

• Fixed channel apparatus. These instruments are able to undertake simulta-neous measurements of several elements (Figure 12.13). The Bragg relation-ship shows that by choosing a crystal (therefore d) and by fixing the angleof detection (and so the value of �), the radiation of wavelength , whichwill satisfy the Bragg conditions, can be isolated. Starting from this prin-ciple several tens of crystal-detector arrangements can be positioned aroundthe same crystal, each coupling �d� ��, defining a unique wavelength that isspecific of a pre-defined element.

Low energy transitions for elements up to phosphorus �Z = 15�, require opera-ting conditions in a vacuum. The resolution can be as low as a few electron-volts. There exists models of this type which are adapted for scanning electronmicroscopes.


X-ray tube

Primary collimator

DetectorFixed detectorreader head (2θ)

Fixed crystalreader head (θ)

θ

2θ

Crystal(grating)

Secondarycollimator

Goniometer

Sample

Crystal LiF 2-0-0

FeKα

FeKβ

NiKβCoKβ

CoKα

NiKα

CrKα

CrKβ

60 80 100 120

kCps

θ Drive

2θ Drive

2 θ Angle

Fixedchannels

Evacuated cabinet

Detector

X-r

ays’

tube

Crystal

Sample

Vacuum

Goniometer

Prim. collimatorSecond. collimator

Figure 12.13 Schematics of two models of crystal-based sequential spectrometers. Above, adiagram inspired from a Siemens’s SR300 instrument. The primary parallel metallic sheetscollimates the X-ray beam emitted by a high power source. The secondary sheets collimatorserves to eliminate all of the diffracted light not parallel with the direction 2� in which thedetector is found. Below is a diagram inspired by the model ARL 9800, uniting a goniometricassembly associated with fixed channels formed from a crystal/detector coupling, for measuringpre-defined elements; right, a typical spectrum of an alloy, recorded as a function of the angle2� in degrees as the abscissa and intensity in Cps as the ordinate (document Philips Analytical).The detectors are of the Geiger–Müller type.

12.5.3 Filter instruments – single channel system

These are robust instruments often installed on site for the continuous monitoringof industrial production sequence. In most of these cases, the object is to measurea single element present in a fabrication process, from a particular and typicaltransition, provided that line can be isolated from the rest of the spectrum.

12.6 SAMPLE PREPARATION 277

One method used to isolate a X-ray line from unwanted background and noise,employs equilibrated filters. It consists of linking the concentration of interest tothe difference between two measurements. The first is obtained by installing atransmission filter between the sample and the detector to isolate the characteristicradiation of the element wanted and the second by fitting an absorption filterwhich is opaque to this same radiation. This will enable, for example, to quantifythe copper from its main spectral line by using two filters, one made of nickel andthe other made of cobalt. The fluorescence originating from the filters themselvesis a limiting factor in this method, which is reserved for routine measurements.

12.6 Sample preparation

Measurements will be repeatable based on the presumption that the sample isinherently uniform in analyte concentration. It is also important to think aboutthe possibility of re-absorption of the emitted fluorescence (the optical quenchingby the elements present).

Absorption by the matrix can provoke either an underestimation of the resultby optical quenching, or an overestimation of the result when some of the X-rayfluorescence causes a secondary excitation of other elements present in the sample.For example, the presence of iron in aluminium provokes an increase in the fluo-rescence because radiation emanating from iron excites in its turn the fluorescenceof aluminium.

Liquid samples do not require particular preparation prior to the analysis. Asmall volume of sample is placed in a type of vial whose bottom is replaced bya film of polypropylene or mylar (polyester) transparent to X-rays, The depth ofabsorption can be as much as 1 cm for hydrocarbons.

Solid samples and especially if the matrix is not known, need transformationprior to the measurement. In fact, the measured fluorescence of these materialsonly concerns a thickness of several micrometres beneath the surface. This thick-ness depends upon its composition and of the angle of incidence of the primaryX-rays: this can be from between several angstroms (if the incident angle is acute),up to half a millimetre. All superficial heterogeneity can have important conse-quences and cause variations in the result. This is the principal reason for surfacetreatment prior to analysis.

The two techniques used for sample preparation of a solid are fusion and pelletformation. Fusion involves mixing a little of the sample, reduced to powder, withlithium tetraborate �Li2B4O7�, and different additives. The glass obtained by fusionin an electric oven by induction heating, called a pearl, constitutes a matrix oflight elements and is therefore transparent to X-rays. Pellet formation, using anhydraulic press, is the alternative to the fusion technique. To ensure the cohesionof the pellet, a wax is added (an organic polymer formed from light elements).


12.7 X-ray absorption – X-ray densimetry

When a beam of X-rays passes through a material the result is an exponentialattenuation of the primary beam. The different possible interaction processes, asfluorescence, are characterized by a probability of occurrence per unit path lengthin the absorber. The flux of transmitted primary photons I after having passedthrough an attenuator with a thickness x (cm) and a linear attenuation coefficientcalled ��cm−1� for the wavelength considered, can be calculated with respect toits initial value I0 and for an angle of penetration of 90 � as follows:

I = I0 · exp �−�x� (12.5)

This relation which corresponds to the integrated form of the expressiondI = −�Idx, is comparable to that discussed in colorimetry (Lambert–Beer law, seeChapter 9). The linear attenuation coefficient � can be calculated for all material forwhich , the density of the medium (g/cm3) and the composition are known.

Individual attenuation coefficients are available from tables for each element.Next, the weighted mass attenuation coefficient �M�cm2/g� must be calculatedfor the material studied from its elemental composition. Finally, � = �M .

Figure 12.14 shows that a film of beryllium, such as those serving as windowsfor X-ray detectors, is opaque to the radiation emitted by the lighter elements (E<1keV for atomic numbers below 10). The linear attenuation coefficient of a mate-rial decreases as the wavelength is decreased. For lighter elements, measurementsare made under an atmosphere of helium while for solids a vacuum is imposed.

Transmission through a film of:1 - beryllium (thickness 7 μm)2 - aluminium (thickness 25 μm)

0,5

% T

rans

mitt

ance

0

20

40

60

80

100

1 2

1 2 10 KeV5

Figure 12.14 X-ray densitometry – examples of percentage transmittance for two films made oflight elements. A 7�m film of beryllium is often used for making windows of energy detectors.For a radiation of 1 keV, (e.g. Na K�) it is noteworthy that the attenuation achieved by thisfilm is still of 50 per cent.

12.9 APPLICATIONS OF X-RAY FLUORESCENCE 279

� Expression 12.5 estimates that a household foil of aluminium film of thickness12 μm ( = 2.7g/cm3) absorbs 57 per cent of the intensity of the transition TiK� (μM =264 cm2/g) but only 1 per cent for the transition AgK� (μM = 2.54 cm2/g).

12.8 Quantitative analysis by X-ray fluorescence

The relationship between the weight concentration of the element to be analy-sed and the intensity measured from one of its characteristic spectral lines is acomplex one. For trace analysis several mathematical models have been developedto correlate fluorescence to the atomic concentration. A series of corrections mustbe introduced to account for inter-element interactions, preferential excitation,self-absorption and the fluorescence yield (the heavier atoms relax by internalconversion without photon emission). All of these factors require the referencesamples to be practically the same structure and atomic composition than thesample under investigation, for all of the elements present. It is mostly becauseof these reasons that quantitative analysis by X-ray fluorescence is difficult toobtain. When operating upon a solid sample, a perfectly clean surface is important,preferably polished, since the analysis concerns the composition immediately closeto the surface.

This method is well adapted to quantitative analysis, where automatic identi-fication of the spectral lines can be made by very sophisticated visual displays.Principal corrections (called ZAF) relate to atomic number �Z�, nature of theisotope �A� and fluorescence �F�. In semi-quantitative analysis, the software cangive an approximate composition of the sample without the need for referencestandards.

12.9 Applications of X-ray fluorescence

Initially, X-ray fluorescence was used in industries treating metals or alloysand in more general in the heavy industry (iron and steel industry, cements,ceramics, glassware). The method is non-destructive, requires little sample prepa-ration beforehand and has a large dynamic range. For example, it is possible tomeasure two elements present in the same sample in which the concentrationsare 50 per cent for one and a few ppm for the other. Progress in the detection ofphotons of high energy has improved the precision for analyses of heavy elements,which can be obtained from their K, and not from their L spectral lines whichare situated in the region of the spectrum where background noise levels are toohigh.


Reading 2NomSec 62.3Super TeachAISI 304Sn 5.29Pd 45.98Ag 37.41Al 84.97Mo 34.67Nb 1.82Zr 1.35[ Cd ]

0.000.000.000.000.000.000.00

Figure 12.15 Portable field apparatus. This instrument represents a category of energy disper-sive spectrometers equipped with an X-ray generator but no radioactive source (reproducedcourtesy of Niton, USA). Type of information that can be obtained.

With the convenience of current apparatus (Figure 12.15), the scope of appli-cation of this technique is considerably broad, either in research and developmentor as quality control in production. It extends from routine qualitative analysesto measurements that can attain the high level of precision of classic methods.Semi-quantitative analyses are possible, using highly efficient computer software.

6 α-rays sources

α

6 α-rays detectors

electronics

R-X

surface ground

X-rays detector

APXS view, above

Figure 12.16 Alpha particle X-ray spectrometer (APXS). To determine the elemental compo-sition of rocks and soils of Martian surface, the rovers, which landed in 2004 on Mars, carry adeployment device that could be in contact with the rocks. The sensor head contains six 244Cmradioactive sources, six alpha detectors and one X-ray detector in the centre. The accumulationtime is a few hours per sample analysed.

PROBLEMS 281

X-ray microanalysis, for which samples must ideally be electrically conductors,allows element mapping in heterogeneous samples, if observed with a scanningelectron microscope (cf. Section 12.3.3).

The list would be very long if all of the analytical applications of X-ray fluores-cence were recorded, photographic industry, paper, semi-conductors (impuritiesof silicon), petrochemicals (S, P, Cl). In geology, toxicology, environment (dust,combustion fumes, pollution), refuse and rejects (heavy elements such as As, Cr,Cd, or Pb), analysis of ultra light elements (nitrogen) and even space exploration(Figure 12.16). Finally, a current application is the use of X-ray fluorescence todiagnose concentrations of lead in the home (paints and wall coverings).

Problems

12.1 A solution is prepared with 8 g of potassium iodide and 92 g of water.

1. Calculate the mass absorption coefficient (�m) of this solutionmeasured with the MoK� radiation of 17.4 keV. Consider that thesolution (volume = 105kg/L) is an equilibrated mixture of thesefour elements (K, I, H and O).

2. What fraction of the Mok� line remains after having crossed 1 cm ofthis solution?

Element �M �cm2/g� Atomic mass (g/mol)

K 162 39I 363 127O 12 16H 04 1

12.2 Find the following classical conversion formulae:

nm = 1240

E�ev�

Å = 124

E�kev�

Recall: h = 66260 × 10−34 J s; c = 2998 × 108 m/s; 1Å = 10−10 m; 1 eV =1602 × 10−19 J.

12.3 An X-ray tube with a tungsten target and which serves as the sourcein an X-ray wavelength dispersive fluorescence spectrometer is equipped


with a crystal of ethylenediamine tartrate. The plane of reflection in usecorresponds to an inter-reticular distance of d = 4404Å.

1. Calculate the angle of deviation measured with respect to the direc-tion of the incident radiation which collects the emission lineL� of bromine ( = 8126Å) of a sample of sodium bromide (itmay be considered that the observations recorded are of first orderreflection).

2. Knowing that the wavelength of the tungsten line K� occurs at0.209 Å, calculate the minimum voltage necessary across the X-raytube, to excite this line.

12.4 Consider a wavelength dispersive instrument provided with a goniometercomprising a rotating topaz crystal of an appropriate size.

1. Knowing that the crystal spacing of the monochromator (303) has aninterplanar distance of 0.1356 nm, calculate the limits of the wave-lengths within which it is possible to record the spectrum if the angleof incidence varies through 10� to 75�.

2. Convert these two values into keV.

12.5 Sulphur presents two lines: K�1 = 537216Å and K�2 = 537496Å

1. What is the energy difference, expressed in eV, between K�1 and K�2?

2. If it is known that the width at the mid-height of these lines is 5 eV,what conclusion can be drawn?

3. If the position of the K�2 line increases by 0.002 Å when passingfrom S6+ to S�, show that this has no impact upon the location ofthis photoelectron in energy terms.

12.6 Is it possible to protect oneself from X-rays by being wrapped in aluminiumfoil of thickness 12�m?

First calculate for the % transmission for the Ti K� line (4.51 keV,�m Al=264 cm2/g), then for the Ag K� line (22 keV, �m Al=254 cm2/g).The volumic mass of the aluminium is 266g/cm3.

PROBLEMS 283

Consider the same question but, in place of the aluminium, a film oflatex is employed �C5H8�n of the same thickness (volumic mass = 1).The final calculation will be made with the transition K� line of titanium(�m C = 256 cm2/g��m H = 043 cm2/g).

12.7 1. Why does the table of X-ray lines only begin with the third elementof the periodic table?

2. Why, when measuring the elements whose energy of emitted radiationis inferior to 3 keV, is it necessary to replace the air in the apparatusby helium?

12.8 When establishing the Bragg equation the difference is calculated betweenthe optical path of two rays incident and reflected, making the same angle,�. Why is this?

12.9 For determining the % mass of Mn present in a rock, the element Ba isused as an internal reference. Two solid standard solutions in the form ofpearls of borax yielded the following results:

No of solution % Mn by mass Ratio Mn/Ba

1 0250 08112 0350 0963unknown sol. ? 0886

Evaluate the % mass for Mn in the original solution

12.10 If a piece of nickel is suspended at a depth of 1 cm in an aqueous solution,what fraction of the intensity of the transition K�, emitted when metalatoms are excited, will reach the surface? Mass attenuation coefficients forhydrogen and oxygen are H: 04 cm2/g; O: 138 cm2/g.

12.11 If the distance between the sample and the detector is 5 cm, calculate the %attenuation of a radiation possessing an energy of 2 keV produced by thepresence of air over this distance. Take 80% nitrogen and 20% oxygen forthe mass composition of air. The specific weight of air is 1.3 g/L. The massattenuation coefficients of elemental nitrogen and oxygen are, for a radiationwhose energy is 2 keV: �m = 494 cm2/g for N and 706 cm2/g for O.

13Atomic absorption and flameemission spectroscopy

Atomic absorption spectroscopy (AAS) and flame emission spectroscopy (FES),also called flame photometry, are two analytical measurement methods relying onthe spectroscopic processes of excitation and emission. Methods of quantitativeanalysis only, they are used to measure of around seventy elements (metal or non-metal). Many models of these instruments allow measurements to be conductedby these two techniques although their functioning principles are different. Thereexists a broad range of applications, as concentrations to the �g/L (ppb) level canbe accessed for certain elements.

13.1 The effect of temperature upon an element

The principle of atomic absorption and flame emission is best understood throughan experiment performed by Kirchhoff more than a century ago in which hedemonstrated that incandescent gases absorb at the same wavelengths as they areable to emit.

When the light of an electric arc (serving as a source of white light), is dispersedby a prism, a continuous spectrum is obtained (Figure 13.1, top). If this radiationsource is replaced by a Bunsen burner onto which a few crystals of sodium chlorideis sprinkled, then an emission spectrum of sodium is obtained which possesses thewell-known yellow doublet located at 589 nm, among other lines (images of theentrance slit, Figure 13.1(middle) and Figure 13.2). This part of the experimentillustrates flame emission. Finally, if the two previous sources, electric arc and theflame of the Bunsen burner are placed in series along the same optical path aspectrum will be obtained which, in contrast to Figure 13.1(top), contains darklines in place of the emission lines of sodium (Figure 13.1, bottom). This is theresult of the presence in the flame of a large proportion of ground state sodiumatoms that can absorb the same frequencies as the excited sodium atoms emit.This is a manifestation of atomic absorption.


286 CHAPTER 13 – ATOMIC ABSORPTION AND FLAME EMISSION SPECTROSCOPY

Collimator Objective lens Screen

ContinuousspectrumDispersive system

Linespectrum(Na)

Continuous spectrumwith dark lines (Na)

Slit

1

2

3

Na

Na

+

Figure 13.1 Kirchhoff ’s ‘line reversal’ experiment. The schematics for the optical set-up (colli-mator, objective), have been simplified for reasons of clarity. See text for explanations.

0

1

2

3

4

5

6

Ene

rgy

(eV

)

Atomic ionisation energy of the atom: 5.14 eV

5 s

4 s

3 s

3 p

3 d

4 p

Resonance lines(yellow doublet)

615.4

616.0

1138.3

330.

3

330.

2

818.3

819.6

589.0589.

6

1140.4

Figure 13.2 Several energy levels of the sodium atom. Simplified representation of the excitedstates in the sodium atom. Origins of the different emission lines, according the selection rules.The values are indicated in nanometres.

13.1 THE EFFECT OF TEMPERATURE UPON AN ELEMENT 287

� Diverse instruments exploiting the principle of this phenomenon are used tomeasure traces of mercury in a polluted atmosphere. A device has been designedthat corresponds to a sort of colorimeter dedicated to this single element. The sourceis a mercury vapour lamp and the measuring cell is a transparent tube filled withthe atmosphere to be monitored. If mercury vapours are present in the optical path,there will be absorption of the radiation emitted by the lamp, a consequence being adiminution of the light intensity in proportion to the mercury concentration.

This experiment illustrates the concept of potential energy states defined for allatoms by their electronic configuration. When an atom in the free state is broughtto high temperature or is irradiated by a light source of the near UV/Vis region,then the probability of one of its outer shell electrons to be promoted from theground state to an excited state is very high. This electron transfer correspondsto an absorption of energy. Conversely, when the atom returns spontaneously toits ground state, it can re-emit this excess of energy in the form of one or manyphotons. Thus, in the preceding experiments, the flame induces the most probabletransitions in the sodium atom (Figure 13.2).

The Maxwell–Boltzmann distribution function permits a calculation of the effectof temperature on each electronic transition. By designating N0 as the number ofatoms in the fundamental state and Ne as those in the excited state, one obtains:

Ne

N0

= g · exp

[−�E

kT

](13.1)

where T is absolute temperature in Kelvins, Ne/N0 is the ratio of the statisticalweights of the ground (0) and excited (e) populations of the element considered(whole number), g is a small integer number which depends of the quantumnumber of each element, �E is the energy difference (joules) between the ground(0) and excited (e) state populations concerned and k is the Boltzmann constant�k = R/N = 1�38 × 10−23 J/K�.

If �E is expressed in eV instead of joules, expression 13.1 becomes:

Ne

N0

= g · exp

[−11600

�E

T

](13.2)

Each atomic transition leads to an emission or an absorption of energy, whichcorresponds on the spectrum to a very narrow interval of wavelength. The uncer-tainty around the calculated value constitutes the natural bandwidth of the spectralline. The width is temperature dependent and can pass from 10−5 nm under idealconditions, to about 0.002 nm at 3000 K. In reality, the line widths as observedthrough the monochromator of an instrument are much greater owing to thecurrent technical limits of spectrometers.


13.2 Applications to modern instruments

To measure an element by one or other of these two methods, it must be in theform of free atoms. To this end, the sample is heated to a temperature of at least2000 �C, in order to dissociate all chemical combinations in which the elementunder study is engaged, including the rest of the sample. This pyrolysis leads to thetotal concentration of the element without distinguishing the different chemicalstructures in which the element was possibly bound in the original sample (thisis therefore opposite to a speciation analysis).

Two thermal devices co-exist: one consists of a burner fed by a combustiblegaseous mixture, the other is a type of small tubular electric oven. In the firstassembly, used for the majority of elements, an aqueous solution of the sample isnebulized and then introduced into the flame at a constant rate. In the second, thesample is deposited in a small graphite hollow rod open at both ends, where it isvolatized. This more expensive assembly has a greater sensitivity toward refractoryelements (V, Mo, Zr). In both methods the optical path source/detector passthrough the region containing a tiny cloud of atoms gas in the free state.

In AAS, as in FES, the measurement of light intensity is carried out at awavelength specific to each element being analysed.

• In AAS, the concentration can be deduced from the measurement of lightabsorption by the atoms remaining in the ground state when they are irradi-ated by an appropriate source of excitation.

• In FES, conversely, the concentration can be deduced from the intensity ofthe radiation emitted by the fraction of atoms that have passed into excitedstates.

� Flame emission spectroscopy is based upon the emission of photons by someelements when they are subjected to a temperature of the order of 2000 to 3000 �C.The technique, which is used solely for quantification, is distinguished from atomicemission. This more general term concerns another method of spectral analysis, bothqualitative and quantitative, using thermal plasma sources to obtain much highertemperatures and holding a far more higher performance optical arrangement.

13.3 Atomic absorption versus flame emission

Current values of the different parameters of expressions 13.1 and 13.2 are shownin Table 13.1 for some elements. Examination of the data reveals that practicallyall of the atoms remain in their ground state when the energy difference �E islarge and the temperature is low.

Therefore it would seem to be preferable, in all circumstances, to base themeasurements upon atomic absorption instead of flame emission, as the absorp-tion spectra are simpler than those of emission. However, the matrix in which the

13.3 ATOMIC ABSORPTION VERSUS FLAME EMISSION 289

Table 13.1 Ratio of Ne/N0 for several elements at various temperatures

Element � (nm) E (eV) g 2000 K 3000 K 4000 K

Na 589 2�1 2 1�0 × 10−5 6�0 × 10−4 4�5 × 10−3

Ca 423 2�93 3 1�2 × 10−7 3�6 × 10−5 6�1 × 10−4

Cu 325 3�82 2 4�8 × 10−10 7�3 × 10−7 3�1 × 10−5

Zn 214 5�79 3 7�3 × 10−15 5�7 × 10−10 1�5 × 10−7

element is found can be the cause of interferences, chemical interactions, insta-bility to the excited states and other phenomena that occur at high temperatures(Figure 13.3) and which render absorbance measurements difficult.

Yet, with the most modern detectors containing a photomultiplier, reliablemeasurements can be obtained as long as the ratio Ne/N0 is greater than 10−7.The experience reveals that flame emission is in fact preferable only for five orsix elements. This is why the alkaline earths, elements giving coloured flames, areeasily measured by emission (Table 13.1).

The value of the ratio Ne/N0 does not imply that all of the excited atoms Ne

return to their initial state as they emit photons. When they fall back down, theycan lose their excess energy by other means. Otherwise, the more the temperatureincreases, the more complex the emission spectrum becomes, mainly due to theemergence of lines originating from ionized atoms (Figure 13.3). To study thesecomplex spectra instruments that possess optics of very high quality are required(cf. Chapter 14).

1 - Evaporation2 - Vaporisation3 - Dissociation4 - Ionisation5 - Reaction6 - Decomposition7 - Recombination

MXAerosol (sol.)

MXSolid aerosol

MX*

MXgas

MOMOH*...

MO*MOH*

M*(Atomic)

M+*M+ + e–

M(Atomic)

AA: Atomic AbsorptionEF: Flame EmissionEA: Atomic Emission

2 3

Abs. Em.

5 6

Abs.

Em.

4 7

1

AA

FE

AE

Figure 13.3 Summary of the possible evolution of an aerosol in a flame. Atomic absorption andemission are represented by the shaded areas of the diagram.


13.4 Measurements by AAS or by FES

The quantification of elements by these two methods implies that a relation existsbetween the concentration and the intensity of the corresponding light absorptionor emission. They make use of protocols which comprise a calibration curve fromstandard solutions of the analyte.

13.4.1 Measurements by atomic absorption

The absorbance of the element in the flame depends upon the number ofground state atoms N0 remaining on the optical path. Measurements are made bycomparing the unknown to the standard solutions.

A = k · C (13.3)

where A is absorbance, C is concentration of element and k is a specific coefficientto each element at the given wavelength.

The method relies on the Lambert–Beer relationship, but the molar coefficientof absorption � is not calculated in this case. The instrument yields the absorbanceby ratioing the transmitted intensities in the absence and then in the presenceof sample. Linearity is only observed for weak concentrations (typically below3 ppm), or for solutions in which the matrix effect is negligible. The methods,comparables to those used in molecular absorption spectrometry, involve classicalprotocols via a calibration curve. If the matrix is complex, methods using standardadditions are used to improve the calibration curve (Figure 13.4).

Abs

orba

nce

Abs

orba

nce

0.0 0.1 0.20.00

0.05

0.10 y = –0.096 x2 + 0.465 × + 0.001

0 0,5 1,0 1,50,0

0,1

0,2

0,3

0,4

0,5

Zn, ppmNa, ppb

R = 0.9999

Figure 13.4 Examples of calibration graphs in AAS. Left, a straight calibration line at sub-ppbconcentrations obtained with an instrument equipped with a Zeeman effect device (seesection 13.7) for the quantification of sodium. Right, a quadratic curve for the measurementfor zinc at concentrations in the ppm range with a burner type instrument. This second graphreveals that when concentrations increase, the absorbance is no longer linear. The quantitativeanalysis software for AAS provides several types of calibration curves.

13.5 BASIC INSTRUMENTATION FOR AAS 291

13.4.2 Measurements by FES

For a population of n excited atoms, the emitted light intensity Ie depends uponthe number of atoms dn that return to the ground state during the interval oftime dt �dn/dt =kn�. Since n is proportional to the concentration of the elementin the hot zone of the instrument, the emitted light intensity Ie which varies asdn/dt, is itself proportional to the concentration:

Ie = k · C (13.4)

This expression is only valid for low concentrations in the absence of self-absorption or of ionization. As previously suggested, to conduct an analysis byflame emission, the response of the instrument requires a calibration with a seriesof standards.

13.5 Basic instrumentation for AAS

In its simplest form, an AAS resembles a single beam spectrophotometer. Theoptical scheme is illustrated in Figure 13.5 which shows a basic model. It containsfour principal components: the light beam issuing from the source (1) passesthrough the burner (2) in which the element is brought to its atomic state beforebeing focused upon the entrance slit of the monochromator (3) which selects avery narrow wavelength interval. The optical path ends at the entrance slit of thedetector (4).

If no sample is present in the flame, the detector will receive all of the lightintensity I0 emitted by the source within this spectral interval selected by the

1

2

34

Dispersive deviceand objective

Entrance slit Exit slit

Signal

AtomisationdeviceS

Detector(PMT)

F F'

Figure 13.5 The diverse components of a single beam atomic absorption apparatus. Model IL157(Thermo Jarrell Ash) constructed during the 1980s. 1, source (spectral lamp); 2, flame burnerwhich provides the atomic aerosol; 3, monochromator grating; and 4, detector (photomultiplier).The source illuminates a slit situated at the entrance the dispersive system. The exit slit, is closeto the detector window. It determines a narrow bandwidth of the spectrum, (�� of 0.2 to1 nm), which must not be confused with either the width of the exit slit or with the image ofthe entrance slit.


White light source Spectral lamp source

Without sampleWithout sample With sampleWith sample

1

2

III0I0

3

4

d λ

1 2 3 4

Figure 13.6 Comparison of transmitted intensities in AAS with a continuum light source(1 and 2), and with a lamp that emits spectral lines (3 and 4). The square region describes thewavelength interval seen by the PMT. The PMT signal is proportional to the white parts in thesquares. In this way ‘the resolution is in the source,’ as expressed by Walsh, who is consideredto be one of the pioneers of atomic absorption.

entrance slit of the dispersive system. Alternately, if the element is present, thedetector receives a reduced intensity I (Figure 13.6).

If the source emits a continuum of light, the ratio I0/I will always be close to1 because the absorption lines are very fine �1 × 10−3 nm�. Such a source wouldswamp the signal. The very narrow absorption band would appear as only a minutechange against the broad incident radiation. However, if a source is chosen whichemits only the wavelengths that the element to measure is able to absorb, theratio I0/I would become much smaller than 1. The second situation is preferable,for it is more efficient to measure a small change in light intensity against a darkbackground, since currently used photomultipliers are extremely sensitive.

13.5.1 Hollow cathode lamps (HCL) and electrodeless dischargelamps (EDL)

For the above reasons, atomic absorption instruments use two basic types of lamps.Hollow cathode lamps (HCL) are discharge lamps that contain a fill gas (argon orneon). Depending upon the element which constitutes the cathode, the emissionspectrum of these sources are different. Hence, to measure an element such aslead, the cathode must contain lead. Each cathode contains the element of choicein a very pure form (99.99 per cent) where possible. This should suggest a majordrawback: different lamps are required for each element to be measured. Thisis why there exist close to a hundred different lamps made from pure elementsas well as alloys or fritted powders for multi-element lamps (Figure 13.7). Theanode is made of zirconium or tungsten and the window of the lamp is made ofeither borosilicate or UV transparent glass for wavelengths shorter than 400 nm.


Cathode Anode Quartz window

Screen

Principle of ionisation

Metal atom

+––––

–––

*

*

–

+

Cathode

Electron

hvNe

Ne

NeNe

Ne

Ne

*

Neon

Excited metalatom

Figure 13.7 Typical model of a hollow cathode lamp. The cathode is a hollow cylinder whosecentral axis corresponds to that of the optical axis of the lamp. The fill gas (normally neon) isalways chosen so that the spectral output of the cathode is free from interference. Right, in thebox, pictorial representation of atoms of the cathode being excited by the impact of neon ions�Ne+�. Hollow Cathode lamps are available as either single element or multi-element dependingon the application. This particularity of AAS renders it impractical to perform qualitative work.

The assembly shown in Figure 13.7 cannot be used for sodium (melting pointtoo low), or mercury (liquid state). For these elements, glow discharge in metallicvapour lamps are used (GDL).

When a potential difference of around 300 V is applied between the electrodes,the electrons provoke the ionization of the gaseous atmosphere within the lamp.These ions (Ar+ or Ne+), acquire enough kinetic energy to strip atoms from thecathode which becomes equivalent, at the surface, of an atomic gas. In callingM(Cat.) the element M in its metallic state (cathode) and M(Gas) when it is inits atomic state, emission corresponds to the following sequence :

M�Cat��Ne+−→M�Gas�∗ −→ M�Gas� + photon

The spectrum emitted by the lamp corresponds to the superimposition ofradiation emitted by the cathode and by the gaseous atmosphere within the lamp.The width of the emission lines, which depends upon different effects (Doppler,Stark (ionization) and Lorentz (pressure)), is narrower than the correspondingabsorption band. The monochromator enables the elimination of a large partof the stray light due to the filling gas, and the selection of the most intensespectral line in order to obtain a better sensitivity (Figure 13.8), except for casesof interference caused by other elements.

An alternative to HCL are electrodeless discharge lamps (EDL) whose light inten-sity is about 10–100 times greater but are not as stable as HCL. They are made ofa sealed quartz tube that contains a salt of the element of interest along with aninert gas. An RF fields is used to excite the gas which in turn causes the metal tobe ionized. These lamps are in general reserved for elements such as As, Hg, Sb,Bi and P.


AsAs

Arsenic hollow cathode lampFiller gas: NeonWindow: quartzMost sensitive line: 197.2 nmSpectral bandwidth: 0.5 nmSecondary line(50% less intense): 193.7 nmSpectral bandwidth: 1 nm.

193.7 nm197.2 nm

0 nm + 2+ 2 – 2– 2 0 nm

Figure 13.8 Characteristic of the arsenic hollow cathode lamp.

� Generally, for each HCL there are several interesting emission lines. Theydo not have the same intensity. The choice of a particular line for an elementdepends, amongst other things, upon the concentration of the solution being nebu-lized, knowing that in AAS the precision of the measurement diminishes fairly quicklywith concentration (dynamic range no more than 1 to 100). The choice of a secondwavelength of weaker absorption avoids the need to dilute a solution when theelement is present in high concentration.

13.5.2 Thermal devices for obtaining atomic aerosols

Atomization using a flame – burner and nebulizer

The atomic aerosol for the instrument is provided by a combination of a nebulizerand a burner. The sample in aqueous solution is sucked up by the Venturi effect.Pressurized air is passed through a tube causing the sample solution to be drawninto the burner as a fine mist where it is mixed with a combustible gaseousmixture to produce a flame, which finally contains the atomic aerosol. Naturally,the sample must be in solution form in order to employ this process. This robustmechanical assembly, called the burner, has a rectangular base of about 10 cm inlength by 1 mm in width. The optical axis of the instrument is aligned with thelongest dimension of the flame (Figure 13.9).

The flame is characterized principally by its chemical reactivity for a givenmaximum temperature (Table 13.2) and its spectrum. This is a complex mediumin dynamic equilibrium, containing free radicals, at the origin of a spectrum inthe near UV which results from the superimposition of emission and absorptionlines. This can interfere with the measurement of some elements. That is why itis not just any flame which may be used for any element. The chemical reactivityof the flame not being homogeneous, it is important to find a good position forthe optical path of the instrument.


Mixing chamber

Burner head

Solution dispersive device

Flow distributor

Nebuliser

Figure 13.9 The burner of an atomic absorption instrument. This type of burner was used inthe Model 3100-3 from Perkin-Elmer (reproduced with permission).

Table 13.2 Upper temperature limits for some gas mixtures

Combustible mixture Max. temperature (K)

Butane/air 2200Acetylene/air 2600Acetylene/nitrous oxide �N2O� 3100Acetylene/oxygen 3400

Often an air/acetylene flame is chosen. To attain higher temperatures the air isreplaced by nitrous oxide, N2O.

Thermoelectric atomization

The previous device with flame and nebulizer may be replaced by a graphite furnacecomprising a tube of graphite with a small cavity that can hold a precise quantityof sample (a few mg or �L using an automatic syringe) (Figure 13.10). This carbonrod, whose central axis coincides with the optical axis of the spectrophotometerbehaves as a ohmic resistor that can attain 3000 K by virtue of the Joule effect. Theheating cycle generally comprises four steps (Figure 13.10). To avoid loss throughprojections the temperature is gradually increased, firstly to dry then decomposeand finally atomize the sample. In this latter step the temperature gradient canattain 2000 �C/s because the sample is brought to the atomic gas state in three orfour seconds.


Model of a graphite tube

Sample

Graphite furnace portArgon

Cooling water

(a) (b)

(c)

Absorbancepeak

Abs.

Time(s)0 10 20 30 40

1 - Drying (100 °C)2 - Decomposition (400 °C)3 - Atomisation (2000 °C)4 - Pyrolysis (cleaning) 2300 °C

0

0,5

1

12

34

500

1000

1500

2000

2500 °C

4 cm

Optical axis

Electrothermal program:

Figure 13.10 The electrothermal atomization device. (a) Graphite furnace heated by the jouleeffect; (b) Example of a graphite rod; (c) Graph displaying temperature programming as afunction of time showing the absorption signal. Two types of measurements can be chosen, thepeak height absorbance or the integrated absorbance (in grey on the figure). The first two stepsof the temperature program are conducted under an inert atmosphere. Solid samples can beassayed.

The graphite tube is surrounded by a double sleeve. One contains an inert gas,such as argon, that circulates to protect the elements from oxidation while theother cools the entire device, using water.

In comparison with the burner, this flameless atomization produces a veryhigh atom density and a longer confinement period which multiplies the overallsensitivity by a factor of 1000.

Chemical vaporization

Some elements such arsenic (As), bismuth (Bi), tin (Sn) or selenium (Se) aredifficult to reduce to atoms in a flame when in higher oxidation states. In orderto measure these elements the sample is reacted with a reducing agent constitutedby sodium borohydride or tin chloride in an acidic medium, just prior to analysis(Figure 13.11). A volatile hydride of the element is formed which is swept up bya make-up gas into a quartz cell placed in the flame of the burner.

13.6 FLAME PHOTOMETERS 297

Pumps

Autosampler

Sample orblank

Gas separator

To the cell

Reaction tube1% NaBH4forAs, Bi, SbSe, Sn, Te,Hg “cold vapour”

Discharge

Des

sica

nt

Burner

Car

rier

gas

(arg

on)

HCL

HCl 5M

B

Blank

Figure 13.11 Schematic of an hydride reactor used for particular elements. This automaticsampling device houses a mixing tube where the hydride of the metal (or non-metal) is formedduring reaction with sodium borohydride. An argon flow extracts the metal hydride formed(gas separator) carrying it to a silica glass tube heated to between 800 and 1000 �C in the flame.

Example of the reduction of an arsenic salt by sodium borohydride:

As+++ NaBH4−−−−−−−→ AsH3

H+�800� C�−−−−−−−→ As + 3

2H2

The metallic hydrides, which are easily thermolysed at around 1000 K, liberate thecorresponding elements in the atomic state. An electrodeless lamp is preferablyused as a light source.

As for mercury, it is not transformed to a hydride but rather remains in themetallic state �Hg0�. Consequently, a special cell that does not require to be putinto the flame is used. This is called the ‘cold vapour’ method, and requiresspecialized instruments (reduction by SnCl2).

13.6 Flame photometers

Measurements by flame photometry are carried out either using atomic absorptionspectrometers with a burner (but without the light source), or flame photome-ters. The latter are less sophisticate instruments whose price is ten time lessthat atomic absorption spectrometers. These photometers are designated to makemeasurements of only five or six elements. They include interchangeable coloured


filters or a basic monochromator that can isolate a spectral band embracing theselected emission line. They are very useful instruments for certain applicationsin quality control such as measurements of alkali metals or alkaline earth metalsin substances (e.g. calcium in beer or milk, potassium in cements, minerals, etc.)More improved models, possess two measuring cells permitting a comparison oflight intensities between the sample and that of a standard, allowing concentrationdetermination. The response linearity is reached rapidly, requiring the use of lowconcentration solutions (10 to 100 ppm).

� The principle of flame photometry is employed in a specific GC detector verysensitive to the element sulfur and also in other specialized analysers. So, in GC,when an organo-sulfur compound is pyrolysed in the burner of the detector, the air–hydrogen flame reduces the compound to elemental sulphur which emits radiation ofwavelength 394 nm.

13.7 Correction of interfering absorptions

Atomic absorption allows the measurement of around 70 elements (seeFigure 13.18). It is widely used because the method can accept samples ofvarious forms at very low concentrations. The scope of applications is thereforeconsiderable. As in visible or infrared spectrophotometry, it is necessary to carryout baseline corrections to eliminate fluctuations coming from the lamp andinterfering absorptions.

Instruments with a burner generally have only low background noise in thesignal.

Alternately, with graphite furnaces, an incomplete atomization of the solid orliquid sample, due to the matrix at elevated temperatures, can produce inter-fering absorptions. This is notably the case with samples containing particles insuspension or difficult to reduce, ions or organic molecules remaining unburnedowing to a lack of oxygen. This gives a baseline of constant absorption (smokes)within the interval defined by the monochromator. To correct this effect, themanufacturers propose improved instruments that allow to apply various methods(Figure 13.12). However, for this type of sample it is not possible to have the matrixalone without the analyte. Particular double beam instruments have thus beendesignated.

13.7.1 Background correction using a deuterium lamp

The model taken as example (Figure 13.13) is a pseudo dual beam optical assemblyto overcome the fluctuations in light intensity of the source and which contains asecond polychromatic source used to determine the absorption due to the matrixalone. This is the most commonly used method.

13.7 CORRECTION OF INTERFERING ABSORPTIONS 299

Figure 13.12 An AA spectrometer, Model AA 280 equipped with a graphite furnace and Zeemandevice. A rotating turret holds height HCL (reproduced courtesy of Varian Inc.)

PMT

Monochromator

D2

50%

50%a

b

a - Sample beamb - Reference beam

1 - Hollow cathode lamp2 - Deuterium lamp3 - Mirror4 - Beam chopper (rotating mirror assembly) 5 - Grating6 - Beam splitter7 - Quartz window

1

2

3

3

33

3

5

4

5

6 777

With HCL

With D2 lamp

absorption:element and backg.

absorption:backg. only

Figure 13.13 Scheme of a AA spectrometer showing deuterium lamp background correction. This‘double beam’ assembly includes a deuterium lamp whose broad emission is superimposed,using a semi-transparent mirror, upon the spectral lines emitted by the HCL. Beam path a passesthrough the flame while beam path b is a reference path. The instrument measures the ratio ofthe intensities transmitted by the two beams and for the two sources. The domain of correctionis limited to the spectral range of the deuterium lamp, being 200–350 nm (reproduced from theoptical scheme of model Spectra AA-10/20, Varian).

For the selected wavelength, using the monochromator, the flame is sweptalternately by light issuing, either from the hollow cathode lamp or from thedeuterium lamp, which constitutes a continuous source. A rotating mirror is used.When the deuterium lamp is selected, bearing in mind that the sample is nebulized


in the flame, only the background absorption is measured since the bandwidthrange is a hundreds of times larger than the absorption line chosen.

When the hollow cathode lamp is selected, the total absorption (background andabsorption due to the spectral line of the element) is measured. Absorbances beingadditive, the difference between the two measurements will yield the absorptiondue to the background corrected sample, whatever the intensities of the two lamps.

13.7.2 Correction using the Zeeman effect

An alternate approach consists in making use of the Zeeman effect. When a freeatom is exposed to a strong magnetic field (10 kG), there is a disturbance ofits electron energy states. This phenomenon, called the Zeeman effect, modifiesthe corresponding emission or absorption spectrum of the element. However, allelements do not respond in the same way. Most frequently, it is observed thateach absorption line is split into three new polarized lines. One of these lines,called component , retains in the initial position, while the two others, namedcomponent � , are symmetrically shifted on both sides of the component (a fewpicometres in a 1-tesla field). The directions of polarization of the and � linesare perpendicular. If a polarizer is installed on the optical path, and oriented inthe direction parallel to the field, only component will absorb the light from thesource. Contrary to the atoms of the element, particles and smoke in suspensionduring the measurement are not affected by the Zeeman effect.

The application of the Zeeman effect in AAS requires the application of anelectromagnet at the graphite furnace (or at the flame). Two assemblies exist forcorrecting the background absorption.

The first set-up is equivalent to a double beam possessing a common opticalpath. It consists of making two comparative measurements with and without themagnetic field. In the absence of magnetic field, the detector receives the light fromthe source minus both the background absorption and the fraction absorbed bythe element being measured : these two absorptions are additive. Alternately, whenthe magnetic field is applied, the absorption band selected separates into severalnew lines. Those whose position has changed can no longer overlap with the lineemitted by the source and they no longer play a role. The line which remains atthe original wavelength (as when there is no magnetic field), is polarized alongthe field’s axis and absorbs the radiation of the source exclusively in this direction.Since the polarizer is installed ‘perpendicular’ to the direction of the magneticfield it will not detect this absorption: the element will have become transparent tothe detector. The detector perceives only the continuous background absorption(Figure 13.14).

The second set-up utilizes a fixed magnetic field and a rotating polarizer ; thesignal oscillates between two extreme values which correspond either to the back-ground absorption alone or to the latter plus the absorption by the componentof the element (Figure 13.15).

13.7 CORRECTION OF INTERFERING ABSORPTIONS 301

Monochromator Detector

PolarizerHCL

Magnetic field

Graphite furnace

Figure 13.14 Correction through Zeeman effect. Modular scheme of an apparatus using thecorrection of absorbance by Zeeman effect. Two solutions are applicable: (1) with or withoutmagnetic field and a fixed polarizer; (2) with fixed magnetic field and rotating polarizer.

Cd emission line at 228.8 nmwithout (1) or with (2) magnetic field

Cd absorption line at 228.8 nmwithout (1) or with (2) magnetic field

Oven

Oven

non-Polarisedsource

π

Background onlyAbsorptionElement + background

Transmitted lightPolariser Measured signalMagn. field

Magn. field

Abs

.

Abs

.

σ+21

nm

Abs

.

Abs

.

1

σ– σ+π

nm

1

2 Specific element absorptionplus background

Background absorption alone

HCL

2

Figure 13.15 Normal Zeeman effect. Pictoral explanation of the rotating polarizer method.

13.7.3 Background correction using a pulsed HCL (Smith–Hieftjemethod)

When the intensity of a HCL is pulsed with high current by reducing the shuntresistance in its electrical circuit, the profile of the emission lines changes. For eachof them the profile broadens, a general consequence of the temperature increaseof the cathode. Moreover, the raised temperature of the cathode produces anevaporation of atoms at the centre of the lamp. This cloud of atoms emitted bythe cathode re-absorbs in a colder part of the lamp as a very fine spectral line. Thenet result is that the emission curve dips in the middle at the same wavelength asthat emitted by the cathode (Figure 13.16).


Hg lamp

PMT detector

Flame

Deuterium arc

4 Hollow cathode lamps

Galvanometer grating drive for line detection

Galvanometer mirror drive for lamp selection

Normal regime Pulsed regime

Emission line shape

Figure 13.16 Pulsed lamp for background correction. The model shown uses the principle ofthe Smith–Hieftje pulsed source background correction. The mercury source as well as theretractable mirrors are used to calibrate the monochromator (reproduced courtesy of ThermoJarrell Ash). Appearance of an emission line of a HC lamp as a function of its voltage.

This self-absorption is the basis of the pulsed lamp technique for correctionof the background absorption. Known as the Smith–Hieftje (S-H) method, thisapplication uses a pulsed lamp which enables a comparison of the two measure-ments. In normal conditions (e.g. 10 mA) and with the sample into the flame,a global measurement representing the sum of the background absorption andthe absorption of the element is observed, while under strained lamp conditions(500 mA) only the background absorption is present as the lamp will no longeremit at the wavelength chosen. The comparison of these two absorbance measure-ments leads, after correction, to the calculation of the absorption due to the soleanalyte.

These three methods of correction present advantages and inconveniences: thedeuterium lamp method uses a more complex optical assembly including a secondsource – the Zeeman method is expensive – the S-H method requires speciallamps. The dynamic range is reduced. The choice of the correcting device mustbe made as a function of the desired applications.

13.8 Physical and chemical interferences

Whenever possible, an element is measured using an intense emission line of thecorresponding lamp. Generally the most intense corresponds to the resonanceline. However, various factors engendered by the matrix can lead to erroneousanalytical results.

13.8 PHYSICAL AND CHEMICAL INTERFERENCES 303

13.8.1 Spectral interference

In AAS, the graphite furnace can be the cause of interfering emissions from thewalls of the graphite rod. The compounds from the matrix can lead equally tounwanted absorptions.

There is never total impossibility of the superimposition of two absorptionlines: such as that chosen for the measurement and that coming from a secondaryline belonging to another element. Confusions are rare but it is sometimesadvisable to undertake a second measurement at another wavelength. In atomicemission this problem is frequent, not least as the spectrum is more complex(cf. Chapter 14).

13.8.2 Superimposition of absorption and emission of the sameelement

A non-negligible fraction of the atoms of certain elements pass to the excited statethermally. These atoms emit photons of the same energy that those remaining inthe fundamental state are able to absorb. In order to correct the measurement (theemitted intensity has to be subtracted) the HCL voltage is pulsed, which permitsdifferentiation between the emission signal, which is constant, and the absorptionsignal, which is pulsed. It is also an easy way to account for instrumental variationsand ‘flame flicker’.

13.8.3 Chemical interactions

When using atomic absorption to search for traces of elements it is important tobear in mind the matrix in which they are found. Well established protocols mustbe followed to suppress ionic or chemical interference. Mineral salts or organicreagents serving as ‘liberating agents’ R are often introduced into the solutions tobe nebulized for corrective reasons. This treatment will effectively liberate elementM from its combination MX, if compound RX is more stable than MX,

R + MX −→ M + RX

� Thus when calcium is to be measured in a matrix rich in phosphate ions or inrefractory combinations containing aluminium, then strontium or lanthanum chlorideare added. The effect sought is to liberate calcium and to increase the volatility ofthe medium to ensure a more efficient elimination during the decomposition step. Inthe same way to measure sodium or potassium it is usual to add a little of Schinkel’ssolution (CsCl/LaCl3).


O

(HO2C-CH2)2N-CH2CH2-N(CH2-CO2H)2 (Acid EDTA)

NaCl + NH4NO3

m.p. = 307 °C (sublimates)m.p. = 800 °COO

NN

NN

OO

OO

OO OO

O

OO

OO2H+

– –

NiNaNO3 + NH4Cl

Figure 13.17 Matrix modification. Ammonium nitrate or EDTA increases the volatilityof certain elements. A volatile complex of type 1 : 1 between a molecule of EDTA and the Ni2+ ion.

With apparatus containing a graphite furnace, ethylenediaminetetraacetic acid(EDTA) is introduced to form 1 : 1 complexes with bivalent ions, or ammoniumnitrate if the matrix contains a high concentration of sodium (Figure 13.17).

Finally, the use of very hot flames can provoke partial ionization of certainelements which decreases the concentration of free atoms in the flame. Thisphenomenon is corrected by addition of an ionization suppressor in the form of acation whose ionization potential is lower than that of the analyte. A potassiumsalt of about 2 g/L is often employed for this purpose.

This variation of the ionization can occur more or less spontaneously when thematrix contains one or more alkaline elements. To avoid these random errors, anionization buffer based upon a potassium or sodium salt is added systematically tothe solutions. An alternative consists to prepare a series of standards in a mediumclose to that of sample.

13.9 Sensitivity and detection limits in AAS

More than 70 elements can be measured by AAS (Figure 13.18). The lowestconcentration that can be quantified in a sample depends upon many factors.In spectrometry the sensitivity for an element is defined as being the concen-tration expressed in �g/L which, in aqueous solution, leads to a 1 per centdecrease �A = 0�0044� in the transmitted light intensity. So, for manganese (Mn),this value is 4 pg with an aqueous matrix. When possible, a calibration curveshould be established with concentrations in the range of 20 to 200 times thisvalue.

The detection limit corresponds to the concentration of the element giving asignal whose intensity is equal three times the standard deviation of a series ofmeasurements made upon the analytical blank or on a very dilute solution (degreeof confidence 95 per cent). In practice, the concentrations must be at least tentimes higher than the detection limit to give reliable measurements.

PROBLEMS 305

IA VIIIA

HM Air/acetylene flame He

IIA xx Atomic number IIIA IVA VA VIA VIIA

Li3

Be4

M N2O/acetylene flame B5

C N O F Nexx Atomic number

Na11

Mg12

Al13

Si14

P S Cl ArIIIB IVB VB VIB VIIB VIII IB IIB

K19

Ca20

Sc21

Ti22

V23

Cr24

Mn25

Fe26

Co27

Ni28

Cu29

Zn30

Ga31

Ge32

As33

Se34

Br Kr

Rb37

Sr38

Y39

Zr40

Mo42

Nb41

Tc43

Ru44

Rh45

Pd46

Ag47

Cd48

In49

Sn50

Sb51

Te52

I Xe

Cs55

Ba56

La57

Hf72

Ta73

W74

Re75

Os76

Ir77

Pt78

Au79

Hg80

Tl81

Pb82

Bi83

Po At Rn

Fr Ra Ac

Ce58

Pr59

Nd60

Pm Sm62

Eu63

Gd64

Tb65

Dy66

Ho67

Er68

Tm69

Yb70

Lu71

Th90

Pa U92

Np Pu Am Cm Bk Cf Es Fm Md No Lw

Legend

Figure 13.18 Elements measured by AAS and FES. Most elements can be measured by atomicabsorption or flame emission by using one of the available modes of atomization (burner,graphite furnace or device for hydride formation). The sensitivity varies from several ppb (Cu,Cd, Cr) to several ppm (the lanthanides). The elements of the table (in white) for which theatomic number is not shown are not measurable by atomic absorption. However, the hybridapparatus AAS/OES containing plasmas as a thermal source, has more recently pushed back thelimits of this method of elemental analysis.

Problems

13.1 If the response of the detector of a flame photometer is proportional tothe concentration of the element heated to a state of excitation, by whatfactor is the signal multiplied when the temperature passes from 2000 K to2500 K?

(Establish the general expression and then apply it to the case of elementalsodium, whose resonance is promoted by a radiation of 589 nm wavelength.)

13.2 Why is it advisable to add ethylenediaminetetracetic acid (EDTA) tomeasure calcium when it is in the form of a phosphate?

13.3 Why is a potassium salt (such as KC1) frequently added when one wantsto measure elemental sodium by flame photometer? Remember that thepotential for the first ionisation of potassium is 419KJ mol−1 while that forsodium is 496KJ mol−1�


13.4 The potassium concentration in a blood serum is to be analysed using amethod of addition and flame emission. Two extractions of 0.5 mL of serumwere taken to create two identical solutions and then both were dilutedfurther with distilled water to a final volume of 5 mL. 10�L of 0.2 M KClis introduced to one of these. The values obtained from the apparatus were32.1 and 58.6 arbitrary units. What is the potassium concentration of theserum?

13.5 An AAS method is employed for the determination of lead (Pb) in a sampleof adulterated paprika by the introduction of lead oxide (of the samecolour). An electrothermal atomic absorption instrument that provides abackground correction based upon the Zeeman effect is used.

0.01 g of the paprika powder is placed in the tube of the graphite furnace.The determination of the area peak absorbance was made at � = 283�3nmfirst in the absence and later in the presence of a magnetic field. The valueof the peak absorption following background correction was 1220 (arbitraryunits). Under the same conditions, 0.01 mL of a solution of 10 g/L Pb ledto a value of 1000 in the same units.

Calculate the % mass of lead in the sample of paprika under study.

13.6 A stock solution of calcium ions was prepared by dissolving 0.1834 g ofCaCl2�2H2O in 100 mL of distilled water and then further diluting by a factorof 10. From this new solution, three standard solutions were prepared byfurther dilutions of five, 10 and 20 times, respectively. The unknown sampleis itself diluted 25 times. Sufficient strontium chloride was then introducedto eliminate any interference due to phosphate ions. An analytical blankcontaining the same concentration of strontium was the first solution to beexamined by the air/acetylene flame. The results were as follows:

Blank 1�5 Ca = 40�1g mol−1

Standard 1:20 10�6 Cl = 35�5g mol−1

Standard 1:10 20�1Standard 1:5 38�5Sample 29�6

What is the concentration (in ppm) of the calcium in the sample?

13.7 Among the numerous commercial derivatives of ethylenediaminetetraceticacid (EDTA), a mixed salt of Zn/Na containing one atom of zinc and twoatoms of sodium per molecule of EDTA is found. This mixed salt presentsitself in the form of a crystallized hydrate. An attempt is described to deduce

PROBLEMS 307

the number of water molecules of this hydrate by measuring the presenceof zinc by atomic absorption. The experimental approach was as follows:

A solution A, is prepared by dissolving 35.7 mg of the hydrate in 100 mL ofwater. 2 mL were then pipetted and diluted again with H2O to a final volumeof 100 mL. This constitutes the sample solution B. The standardisation isthen performed with five solutions of known zinc concentration. (see tablebelow).

1. To effect this measurement the slit bandwidth of the atomic absorptionapparatus is 1 nm. What does this parameter represent?

2. Knowing that the calibration curve computed by the apparatusindicates that A = 0�3692, C = 0�99mg/L, calculate the number ofmolecules of water in the mixed salt hydrate of Zn/Na.

3. From the data and by the method of least squares derive an equationfor the calibration curve. Calculate the zinc concentration in solu-tion A. Recall: H = 1�01; C = 12�01; N = 14�01; O = 16�0; Na = 22�99and Zn = 65�39g/mol respectively.

4. Is the use of the standard calibration curve justified for atomicabsorption?

Solution Conc. Zn mg/L Absorbance

Blank 0�00 0�0006Standard 1 0�50 0�2094Standard 2 0�75 0�2961Standard 3 1�0 0�3674Standard 4 1�25 0�4333Standard 5 1�50 0�4817Sample C? 0�3692

14Atomic emission spectroscopy

Analysis by atomic emission spectroscopy constitutes a general method formeasuring elements on the study of the radiation emitted by their atoms presentin an excited state, usually following ionization. Several procedures are used tobreak down the samples into their constitutive elements, most notably by the effectof high temperatures plasmas, spark sources or glow discharges. The emissionbeing far more complex than those of flame emission, instruments required veryhigh quality optics to resolve interferences from both spectral lines and matrixeffects. Since this method measures optical emissions with optical spectrometers,the abbreviation OES is better than AES and will be adopted in this chapter.

Employed since its beginning in metallurgical industries, OES, whose analyticaldomain covers an extended dynamic range, has become an indispensable tool ofchemical analysis. The spectrometers are capable of routinely analysing severalelements either simultaneously or sequentially. A single instrument can performthe functions of several analytical techniques including X-ray fluorescence, atomicabsorption and combustion analyzers. The technique coexists with AAS with whichit is more complementary than competitive. This spectroscopy is less expensivethan mass spectrometry when applied to elements (ICP-MS) though it is notadvisable for the analysis of the lighter elements.

14.1 Optical emission spectroscopy (OES)

When a chemical element in the atomic state is exposed to appropriate conditionsof excitation, it emits a characteristic radiation. On this observation is based ageneral form of elemental analysis, both qualitative and quantitative. This opticalemission spectroscopy issued from sample is very complex and leads to spectra withthousands of spectral lines accompanied by a continuum background.

The instruments designed for these analyses comprise several parts: the deviceresponsible for bringing the sample in the form of excited or/and ionized atoms(based on gas plasmas, sparks or lasers), an high quality optical bench whichconditions the analytical performances, a detector with a sensor (PMT or diode


310 CHAPTER 14 – ATOMIC EMISSION SPECTROSCOPY

Source(ionisation/excitation)

Dispersive system(180 to 800 nm)

Detection(analysis)

Sample

Figure 14.1 Atomic emission spectrometer. Basic concept and an example of a bench model ofspectrometer, the Vista-Pro, CCD simultaneous ICP-OES (courtesy of Varian Inc, USA)

array) and finally a computerized section essential to control the entire instrument(Figure 14.1).

The characteristic that most distinguishes these spectrometers from AA or FEinstruments is their optical bench and sometimes their impressive size. They arereserved to analytical laboratories that have to treat a great deal of samples.

14.2 Principle of atomic emission analysis

As in FES, the light source of the spectrometer is nothing other than the sampleof which all the atoms have been excited. Qualitative analyses of unknowns cantherefore be made. This marks an important difference from atomic absorption inwhich measurements can only be made for elements for which the instrument hasbeen customized (choice of the hollow cathode lamp). From a single run, a multi-element analysis can be obtained in strict contrast to AAS. However only elementsfor which a calibration has been carefully undertaken can really be measured.

Each atom, once in the excited state can lose its excess energy by emissionof one or several photons of which the energies can have many different values(Figure 14.2). For a sample, the dispersive system discloses radiation of a multi-tude of different wavelengths and intensities. For a given sample, the matrix (all

14.3 DISSOCIATION OF THE SAMPLE INTO ATOMS OR IONS 311

λ1

α β γ δ

λ2

λ3 λ4

270 300280 290nm

a chromium saltExcitation

Ion groundstateExcitedstates

Ground state

Visible iron spectrum

EmissionIon excitedstate

M0

M*

M*+E

Figure 14.2 Energy transitions in OES. For every atom there exists hundreds of possibilitiesby which it may returns to the ground state, each of these having its own probability. Even thesimplest sample is containing an enormous number of emission lines. An example (right) is apartial spectrum of an aqueous solution containing a few ppm of a chromium salt and a visiblespectrum of iron.

elements present in the solution) will also emit, therefore the identification ofa particular element that is present only as an ultra-trace, will be obtainable tothe condition that measurements use multiwavelengths to construct the samplefingerprint. More than 75 elements can be determined in as little as one minute.

OES requires high performance instruments capable of locating weak intensitylines in close proximity to other much more intense. This is why preference isgiven to spectrometers having a broader dynamic range.

� FES, which is used for measuring a small number of elements, is of much simplerdesign. For example, when sodium is analysed with a flame photometer whose flameattains 2000 �C, the sodium atoms are practically the only ones emitting radiation.To measure the emitted light, a simple optical filter put between the flame and thedetector, in the absence of a monochromator, isolates a rather broad spectral bandincluding the yellow radiation emitted by the element.

14.3 Dissociation of the sample into atoms or ions

To convert a sample to free atoms, excited or ionized, various procedures areemployed based upon gas plasmas, sparks, lasers or glow discharges.

14.3.1 Gas plasma excitation

The most common instruments for OES contain a plasma torch (inductivelycoupled plasma – ICP) that can reach temperatures of up to 8000 K. This device iswell adapted to samples in aqueous solution.


A plasma is a highly energized ‘cloud’ of gaseous ions and their electrons.Considered to be the fourth state of matter, it is formed by isolated atoms inequilibrium between their neutral and their ionized states (more than 2 per cent)and with the associated electrons �1018/cm3� which assure an overall neutrality ofthe medium.

To initiate the plasma, a flow of argon, weakly ionized by sparks (Tesladischarge), passes through an open quartz tube situated on the axis of several turnsof a water-cooled copper tubing (Figure 14.3). This conductive coil is connectedto a radiofrequency generator (typically 40.68 MHz and with a power of 1–2 kW).

4000 K

6000 K

8000 K

Interface device

Argon

Cold watercirculation

Circulation of the electronsunder the effect of the induced fieldwithin the heart of the plasma

Nebuliser flow

Fibre optic

Load copper coil(with watercooling) Metallic cone Plasma torch end

Plasma

Microwaves

Helium

Discharge tubeWindow

Cold water

Insulator

hν

Water

Auxiliary flow(argon)

Injector tube

Plasma flow(ionised argon)

Figure 14.3 Plasmas obtained by inductively coupling or by microwaves. (a) Above left, (radialviewing to collect radial light). A radiofrequency current (between 27 and 50 MHz) that inducescirculation of electrons in the inert gas drives the torch. The inner tube is used to inject thesample into the plasma. Right (for axial viewing), cooled device using fibre optic. The torchmay consume up 10 to 15 L/min of argon, which serves simultaneously as the ionization gas,nebulization gas and cooling gas (to avoid the torch melting!). (b) Below is a microwave plasmaused at the outlet of a gas chromatograph for a specialized detector. These plasma sources mustbe stabilized for better reproducibility of the analyses.

14.3 DISSOCIATION OF THE SAMPLE INTO ATOMS OR IONS 313

The variable magnetic field that is created confines the ions and the electrons to anannular path. As the medium becomes more and more conducting, by appearanceof an Eddy current, temperature increases considerably by the Joule effect. Thedevice behaves similar to the secondary coil of a short-circuited transformer. Theplasma is isolated from the torch wall by a gaseous sheath of non-ionized argon,which is injected by an external tube concentric to the previous one and is usedto keep quartz wall cool.

The temperature of the plasma varies from 2000 to 9000 K, dependingon the position. By comparison, the flames used in FES are relatively coldsources. Micro-volumes of sample solutions are introduced at a constant flowwith a pneumatic nebulizer via a third tube of small diameter directly intothe inductively coupled plasma. The position in the plasma chosen for themeasurement of light emission (either radial or axial), depends upon theelement and whether an ionic or atomic spectral line is selected for themeasurement.

The ICP torch exerts a double action on the atoms: it excites them, which leadsto photon emission and ionization. This is why the device is found in elementalanalytical methods such as inorganic mass spectrometry, ICP-MS (cf. Sections 16.9and 16.11). In all cases the sample must arrive in the form of droplets whichdo not exceed a few microns in diameter. To this end a nebulizer containingtwo inlets is used, one for the sample solution, the other for a gas serving togenerate the aerosol. The choice depends upon the flow rate required and theionic concentration of the solution (Figure 14.4).

14.3.2 Excitation by sparks or laser

Besides plasmas, which occupy the front rank of atomization and thermal exci-tation devices, other procedures are used. They gather electrical arcs or sparks(between 3000 and 6000 K) for conducting samples, or pulsed lasers. These areabrasion methods which have much progressed and which are used in indus-trial analysis (foundries, cement works). They can be adapted to different opticalassemblies in current apparatuses (Figures 14.5 and 14.6). The UV laser ablation,which leads equally to the production of sparks (even a plasma) at the surface ofthe studied material is regarded as a ‘general purpose workhorse’. The deliveredenergy densities are sufficient for all sorts of samples geological, biological andenvironmental specimens.

� Removal by a repetitive sparking device can be used as a means of producingan aerosol from the surface of the sample. Matter volatilized at the point of impactof the sparks (around 1 mg/min) is then directed by an argon flow to an ICPtorch operating under argon having an applied voltage of between 20 to 50 kV.Otherwise, the light emission collected as a consequence of the sparks leadsto a spectrum of ionic lines while with continuous arcs, neutral atomic lines areprovoked.


Gas

GasSolution

1

2

3

Gas

Solution

Solution

Figure 14.4 Nebulizers. Models: cross flow (1), concentric (2) and parallel (3). In contrast tomodels 1 and 2, model 3 is not subject to particulate obstruction by impurities in the solution.They leave through a large capillary that drains by gravity along a V-groove design to the outletwhere the aerosol is produced (Babington nebulizer). For the solution, a pump regulates theflow of the aerosol. The chamber at the outlet of the nebulizer is used as a drain to eliminatethe larger droplets by gravity.

Counter-electrode

Sample

Graphite electrode

(a) (b)

(c) (d)

–

+ ( – )

( + )

Vacuum system

Pressure 10 Torr

Sample table

light path

anode

cathode

Argon

Sample

Glowdischarge

AAS

OES

M0I0

M* hγ

Laser

Argon

OESHe

Sample

Figure 14.5 Ionization by sparks and glow discharge. (a) Continuous current arc (‘globular’technique). The electrodes are submitted to a continuous voltage of several tens of volts �I =10–20A�. The use of graphite electrodes is at the origin of emission lines due to radicals andother ‘primitive’ organic molecules (nitrile (CN) bands between 320 and 400 nm) as well as acontinuous background. (b) Cell for glow discharge. The sample is placed on the front surfaceof the lamp, creating an enclosed region that is filled by a low argon pressure. The plasmaconfined near the anode, leads to the excitation of the atoms ejected from the sample surface.(c) Schematic of an excitation by UV laser. (d) Glow discharge and laser ablation can also beused for AAS, as a great majority of atoms (M) subsist in the fundamental state M0.

14.4 DISPERSIVE SYSTEMS AND SPECTRAL LINES 315

Figure 14.6 Atomic emission instrument with spark ionization. Left, Jobin-Yvon model JY-50. Details of the spark chamber in the open position. Right, mobile post of Metorex ARCMet-900 industrial analysis. The spark is produced by a gun, linked by an optical fibre to thespectrophotometer situated in the console (reproduced courtesy of Jobin-Yvon and AmericanStress Technologies).

14.3.3 Excitation by glow discharge (GD)

If the sample is a bulk solid sample and is an electrical conductor, it is possibleto use it as the cathode of a kind of spectral lamp whose functioning principleis identical to that described for a hollow cathode lamp (cf. Section 13.5.1 andFigure 14.5). The atoms sputtered and removed from the surface of the sampleare excited by the plasma. This GD-OES technique provides a rapid and accuratesurface analysis, less susceptible to matrix effects and sample homogeneity. It hasthe advantage of yielding spectra with low background levels whose emission linesare narrow since atomization takes place at lower temperatures than that of theprevious techniques.

14.4 Dispersive systems and spectral lines

The active part of the optical set-up begins with the entrance slit onto which isfocused the light produced by the sample (the light source). The width of this slitis regulated by a mechanical system and cannot be less than a few micrometersbecause a minimum of light is required to enter, but its length can attain severalcentimetres.

The source is thus transformed into an luminous object of linear profile ofwhich the optical system of the instrument gives as many defined images – thelines – as there are different wavelengths in the source. Each line corresponds toan almost monochromatic image of the entrance slit of the spectrophotometer.A single element can generate more than 2000 lines.


The lines are distributed in the focal plane as a succession of parallel andvery narrow luminous segments. The width of these lines depends on severalfactors.

There are technical causes characteristic to the instrument and collectivelyknown as ‘instrumental parameters’: width of entrance slit, quality of the optics,focal distance, diffraction phenomena through narrow orifices. However, thereare also causes due to quantum mechanics, which ensure that the spectral tran-sitions have a ‘natural width’. The radiations emitted by the atoms are not quitemonochromatic. In particular with the plasmas, a medium in which the collisionfrequency is high (this reduces enormously the lifetimes of the excited states),Heisenberg’s uncertainty principle plays a large role (Figure 14.7). Moreover, theelevated temperatures increase the speed of the atoms, enlarging line widths bythe Doppler effect. Finally for all of these reasons, the width of the lines at 6000 Kreaches several picometres.

To locate the specific radiations of an element to be quantified (the differentanalytical lines) an optical bench of very high quality is required. These apparatusescan be divided into spectrographs and spectrometers (Figure 14.8 and see alsoFigure 9.12). As above pointed out, the source illuminates a slit which becomesa luminous object, which will be analysed by a dispersive system containing agrating (planar, concave or echelle).

At the beginning, the qualitative study of these spectra was made by visualcomparison using spectrographs. Nowadays these have been replaced by spec-trometers capable of resolving line interferences and problems linked to matrixeffects. Each element, whether in neutral or ionized form, is responsible for a rangeof lines of variable intensities. The instrument is therefore programmed to bothidentify and to quantify the elements in the sample to be measured. Instrumentsare classified into two major groups.

Emission

E1 ΔE1 = 0

ΔE2 > = hν / 2πΔt

E

ΔE2

Figure 14.7 Line width. Representation of a transition between a stable ground state, whoselifetime is infinite and an excited state, which has a very short lifetime. The uncertainty �E2

leads to an imprecision of the corresponding wavelength.

14.5 SIMULTANEOUS AND SEQUENTIAL INSTRUMENTS 317

Concave grating Rowland circle

Sample(Source)

Returnmirrors

photomultipliers

Measurementelectronics

Entrance slit

Exit slits(10 to 30 μm)

Figure 14.8 Optical schematics of an instrument with a concave grating and a polychromatorwith long focal distance. Reflecting mirrors can be used when lines to be detected are too closeto one another. Several polychromators are sometimes associated. To the right, the principleof Rowland’s circle. The optical part of these instruments must be assembled on a very stablemetallic support.

14.5 Simultaneous and sequential instruments

Two large families of instruments can be distinguished of which one to measureseveral elements simultaneously, while the other to measure elements sequen-tially. Present trends favour systems of the first category with fixed optics toundertake pre-defined applications. The disadvantage of these turnkey solutionsis their inability to make an exhaustive analysis of an unknown sample. Thesecond category corresponds to sequential spectrometers in which the detector isfixed and receives only the radiation selected by the monochromator (comprisinga motorized optical grating). By consequence this system only permits themeasurement of the intensity of one line at a time. Measurements of light intensityby photomultipliers are possible over a very extended dynamic range. Elementscan therefore be quantified for which the concentrations, or alternately, the lightintensities of the lines are very different.

14.5.1 Fixed optic apparatus containing a polychromator

For each predefined element, the intensities of one or several spectral lines aremeasured, which constitute the analytical lines of measurement. Each line corre-sponds to a channel which impinges on its own photomultiplier. If the instrument


contains a concave grating, the entrance and the exit slits must be situated on theRowland’ circle, at a tangent to the grating and of which the diameter is equal tothe radius of the curvature of the grating (Figure 14.8). In this kind of instru-ment, which has been abandoned, it was not easy to place several detectors, so thepreferred type of construction has become that described below.

In a single analysis, close to 20 elements can be measured rapidly. Correctionof background noise is also possible by the simultaneous determination of severallines belonging to the same element. The linearity of the measurements extendsover a broader range than in atomic absorption.

14.5.2 Fixed optic, echelle grating apparatus

Another type of assembly comprises the combination of a particular class ofgrating, called echelle grating with a prism focusing device. This leads to a doubledispersion of the light both horizontally, due to the grating and vertically by aCaF2 prism. This arrangement of high optical resolution, whose focal distancecan attain several metres, is an order-separating device. It permits the simul-taneous observation of an extended spectral range, for example 200–800 nm(Figure 14.9).

� For an echelle grating the incident light arrives perpendicular to the sides of thegrooves which are fewer than for a conventional grating (e.g.100 per millimetre)(Figure 14.9). The observation of the diffracted light is made almost at the sameangle, in auto collimation, which maximizes the transmission of light (Littrow conditionfor a blazed grating when the input and output rays propagate along the same axis).Calculation reveals that for a given observation angle a succession of monochro-matic wavelengths are found to superimpose as a result of the large interval sepa-rating two successive grooves. This multiplexing phenomenon (superimposition ofthe different orders n of the grating – n is around 100) is resolved by a prism thatuses the second dimension of the focal plane to separate the different monochro-matic images of the entrance slit. The spectrum remains stationary with respect to theoptical assembly.

At the end of the optical path, dispersion of the ‘lines’ is detected on a matrixof sensors for which the response furnishes quasi-simultaneously informationconcerning thousands of spectral stains (Figure 14.10). So, analyses are undertakenmore rapidly. By a series of improvements, the dynamic range of these sensorshas become equivalent to that of photomultipliers.

14.5.3 Wavelengths scanning instruments (monochromator type)

In contrast to the preceding instruments, the dispersive system is movable in orderto focus the different wavelengths on the fixed exit slit. A motor allows the pre-programmed selection of the wanted wavelengths and the sequential examination

14.5 SIMULTANEOUS AND SEQUENTIAL INSTRUMENTS 319

Images of the entrance slitsuperimposition of n ordersof the grating

Echelle grating

Argon plasma torch

Entrance slit

Dis

pers

ion

(Y)

due

to th

e pr

ism

Dispersion due to the prism(y direction)

2-Dimensional dispersionof spectral lines in the focal plane

Blue

Red

Echelle grating Conventional grating

d(sin α ± sin β) = nλ

αβ

θ d

αβ

θ d

Dispersion (X) due to the grating

Mirrors Mirrors

X

Y

nn + 1n + 2...

prism lens

Figure 14.9 Principle of dispersion in the focal plane of an assembly associating an echelle gratingand a prism. For clarity, the associated optics (collimating and focusing lenses) have not beenrepresented. Comparison of an echelle grating with a conventional grating. The angle reflectingmost of the light of the grating is referred to as the ‘blaze’ angle �. The basic formula indicateswhich are the wavelengths diffracted by the grating at an angle of incidence �, with reference toa grating perpendicular and at an observation angle � (the sign is + if the observation is fromthe same side as the incident beam with respect to the perpendicular and sign – in the contrarycase). The resolution can attain that of an apparatus which would elongate the spectrum over2 m focal length.


Collimating mirror

Plane mirror

Source (Argon plasma)

Source mirror

Echelle grating

Prism/Lens

Focal plane

Entrance slit

Aperture plate

y

x

x

y

1

2

3

4

5 6

7

8

Figure 14.10 Optical scheme for a spectrophotometer with an echelle grating. For clarity onlythe central section of the beam issuing from source 1 is represented (this beam should cover thewhole mirror 2). The echelle grating 5, separates the radiations arriving from the source in thehorizontal plane (in x). The prism then deviates the radiation in the vertical plane (in y). Thepath of three different spectral lines is shown. The images of the entrance aperture 2 are in thefocal plane 8. In the past, to detect these radiations, photomultiplier tubes (PMT) of reducedsize were installed in specific places, but now charge transfer devices (charge coupled or chargeinjection devices, CCD/CID) are used, as an electronic equivalent of photographic plates. Thisallows a continuous spectral cover from 190 to 800 nm with excellent resolution. Sensors of500 × 2000 pixels (each 12 × 12�m) are now used.

of the spectral lines. The light issuing from the source is analysed either by anEbert assembly (cf. Section 9.2), or by a Czerny–Turner dual monochromatorin order to obtain very high spectral resolution (a few nm), comparable to theemission linewidth at this temperature, over a broad spectral region (160–850 nm).Several assemblies of this type can be placed in series to constitute dual or triplemonochromators of very high performance without rendering the assembly toodemanding in volume.

These instruments are notable for their flexibility. A mercury vapour lightsource serves as a means of internally calibrating the wavelengths in order torapidly determine the position of the grating with the greatest precision. Theoptical path is maintained in an enclosure maintained under vacuum. Here againthe proximity of certain spectral lines necessitates a rigid assembly of a greatmechanical precision.

14.6 PERFORMANCES 321

14.6 Performances

Rapidity and detection limits below 1 ppb �10−9� for many elements, make OESone of the best methods of elemental analysis. With instruments containing onearray detector it is possible to record in a few seconds the whole spectrum in highresolution (e.g. several thousands emission spectral lines).

Some spectrometers accept more readily dominating matrices as mud or soils forwhich the elements Si, Fe and Al are in very high concentrations. Each applicationshould be considered as an individual case.

14.6.1 Sensitivity thresholds and detection limits of thespectrometer

The threshold of sensitivity varies according to the instrument and the elementbeing considered. Numerous comparative tables on detection limit values existwhich are continually being updated as a result of the progress made in instru-mentation. The sensitivity threshold corresponds to the minimum concentrationof element in solution that will yield an analytical signal for which the ampli-tude is equal to three times the standard deviation calculated for an analyticalblank. This classic definition leads to rather optimistic values and very variablewith respect to the element. The detection limit of the instrument represents theconcentration of an element, which allows detection with a confidence of 95 percent (cf. Chapter 22).

� The detection limit for a methodology is of more importance than the detectionlimit above. Generally measurements are done in a domain of concentrationcorresponding to 50 times the detection limit of an instrument. When measuringultra-traces quantities, it is obvious that sample preparation requires reagents andwater of very high purity.

14.6.2 Resolving power

Spectral resolution can be determined directly through an experimental measure-ment from a recorded spectrum. This corresponds to the chosen emission peakwidth �, measured at the half-height using the units of the spectrum. Its valuedepends upon both the dispersive system, the wavelength and the instrumenttuning.

The resolving power of a spectrometer is its ability to separate adjacent spectrallines. This theoretical concept is given by the dimensionless parameter R suchthat:

R = /� (14.1)


� is the difference in wavelength between two spectral lines of equal intensity.Two peaks are considered resolved if the distance between them is such thatthe maximum of one falls on the first minimum of the other. Atomic emissionapparatus have resolving powers in the order of 30 000 rising to 100 000. The useof a too wide exit slit (bandwidth arriving on the photo-multiplier tube) reducesthe resolving power of the spectrometer.

14.6.3 Linear dispersion and bandwidth

Linear dispersion defines the extent to which a spectral interval is spread outacross the focal field and is expressed in nanometre per millimetre (nm/mm) –(or its inverse, the reciprocal dispersion in mm/nm). Linear dispersion is asso-ciated with an instrument’s ability to resolve fine spectral detail. It dependsof several parameters such as the focal distances and the widths of entranceand exit slits of the instrument. In general the better the dispersion thegreater is the physical separation distance between two given wavelengths(Figure 14.11).

200 400 600 800 1000 nm100 200 300 400 500

66.6 133.3 200 266.6 333.3

order1st2nd3rd

Linear dispersionat central wavelength

e.g.

10 nm/mm5 ”3.3 ”

λ

λ

αΙ0

Ι0

400 800 nm

collimatingsystem

reciprocal dispersion: 5 mm/1 nm642 643 nm

5 mm

bandwidth is app. 0.2 nm

grating

Figure 14.11 Linear dispersion and order of diffraction. Simplified schematics

14.7 APPLICATIONS OF OES 323

For example if one instrument disperses a 0.1 nm spectral segment over 1 mmwhile the other takes a 10 nm spectral segment and spreads it over 1 mm, finespectral details would be more easily identified with the first instrument than withthe second.

The bandwidth, which must not be confused with the width of the slit, is theinterval of the spectrum, in picometres, which corresponds to the width exitingfrom the slit. This interval is normally broader than the width of the line on whichit is centred.

Thus, if the exit slit is 20�m and if the reciprocal dispersion is of5 mm/nm, the bandwidth will be equal to 1 × �20 × 10−3�/5 = 4 × 10−3 nm,being 4 pm.

14.7 Applications of OES

The large number of elements measurable by OES renders this method of analysisindispensable since it permits the measurement of elements chosen in advance orthe identification of elements present in any sample. Beyond industrial analyti-cal applications – for example, monitoring the wear of car and jet enginemotors, without disassembling them, by measuring the metals present in theoil – it is in the environmental area, without doubt, that analyses are the mostwidespread.

Applications to the analyses of vegetal or animal production (meat, milk), water,air (dust and ash discharges by incinerators), or of soils in which elements arepresent over a wide range of concentrations (spreading of industrial sludges onagricultural land) are also common. This methodology has equally a variety ofapplications in the forensic sciences or in clinical medicine (analysis of tissues orbiological fluids). The advantage of OES is the linearity of response over a verylarge range of concentrations, which enables the treatment of complex matriceswith a minimum of preparation. It is frequent that a single solution allows to passfrom the measurement of one highly concentrated element to another, presentonly as a trace.

Detection by flame photometry has been used for a long time in GC fordetermination into compounds containing phosphorus or sulfur. Starting fromthis principle, high temperatures generated by gas plasmas can be employed todestroy the compounds eluting from the column while information concerningtheir elemental composition is collected by hyphenating an atomic emissionspectrometer with the chromatograph (Figure 14.12). This is the GC/ICP-OEStechnique.

By choosing a specific line of an element, a selective chromatogram can beobtained of all of the compounds eluted that contain this element. This is thedomain of speciation analysis, the search for classes of compounds correspondingto an association of several elements. This approach avoids interferences due to thesample matrices. It is disappointing that this method of identification of organic


Gas phasechromatograph (GC)

Microwaveplasma device

Polychromatordetector

HeliumMicrowave

plasmaGrating

Diode array

GC column1

2

3

Diffractinggrating

herbicides

Retention time (min)

N

S

C

F

Br

0

H

CI

0 2 4 6 8 10 12 14 16

Figure 14.12 Coupling of a gas chromatograph with an atomic emission spectrophotometer. Theeffluent from the capillary column is injected into a plasma, which effects the decompositioninto the corresponding elements. Each chromatographic signal corresponds to a compoundcontaining the element being studied. This is the principle of speciation analysis (chromatogramstaken from a Hewlett-Packard document).

molecules implies sample destruction, leaving only information concerning itselemental composition: during this ‘chemical butchering’ the structural informa-tion is lost.

Problems

14.1 1. Why do the elements which are measured lead to atomic emissions ofrelatively low intensity?

2. Why does one generally observe ionic emissions?

14.2 When an atom emits radiation, the frequency of the corresponding photonis linked to the energy of the levels between which the transition occurs.According to the Heisenberg principle, if the excited state has a lifetime of�t, then this results in a minimum uncertainty for the energy �E, suchthat: �E�t ≥ h/2.

PROBLEMS 325

From this equation calculate the natural width of the 589 nm emissionline for sodium if �t = 1ns.

14.3 Five standard solutions were prepared for measuring the lead concentrationin two solutions, A and B. The two solutions A and B contain the sameconcentration of magnesium used as an internal standard. The followingdata were obtained:

Conc. (mg/L) Emission of signal (arbit. units) Signal of Mg

0�10 13�86 11�880�20 23�49 11�760�30 33�81 12�240�40 44�50 12�000�50 53�63 12�12sol A 15�50 11�80sol B 42�60 12�40

From the data, calculate the lead concentration (mg/L) in the two samplesolutions, A and B.

14.4 The resonance level of the sodium atom is sometimes said to be 16960 cm−1

from the fundamental level. From this value calculate the correspondingwavelength and the energy of the transition associated with it.

14.5 Explain why it is easier to measure traces of radioactive, �-emitting isotopesof long half-life by ICP/MS rather than by radioactivity counting.

14.6 If the linear dispersion of a spectrograph used in OES is 2 mm for adifference in wavelength of 1 nm and the size of the exit aperture is20�m, calculate the spectral bandwidth reaching the detector.

15Nuclear magnetic resonancespectroscopy

Following on from the pioneering work of physicists Bloch and Purcell around1945 nuclear magnetic resonance (NMR) very quickly became a flexible andirreplaceable method of spectroscopy for a variety of areas in chemistry. NMRis a powerful and theoretically complex analytical tool that allows the study ofcompounds in either solution or in the solid state and serves equally in quantitativeas in structural analysis, though it is especially in the latter where it is very efficientin gathering structural information concerning molecular compounds. It is there-fore of particular practical importance to organic chemistry and biochemistry.Used as a complementary technique to methods of optical spectroscopy and massspectrometry, it leads to precise information concerning the structural formula,stereochemistry and in some cases the preferred conformation of molecules andeven to the identity of the compounds studied. For all of these reasons, NMRhas become one of the principal study techniques for inorganic crystals as wellas molecular structures. Although NMR has for a long time been considered asnot sensitive enough to be adaptable to environmental analysis, this situation haschanged, particularly in view of the linking of liquid chromatography with NMRspectroscopy.

15.1 General introduction

Nuclear magnetic resonance has given its name to a very remarkable method ofsolving the problems of structural determination for organic compounds and forcertain types of inorganic material. NMR spectrometers are therefore often locatedin research laboratories although more trouble-free instruments exist exploitingthe same principles for routine applications (see Figures 15.32 and 15.33, at theend of this chapter).

This method for studying matter can be described by choosing solely relevantexamples from organic chemistry, the elucidation of molecular structures having


328 CHAPTER 15 – NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY

-CH2- CH3-CH2-Inte

nsity

(arb

. uni

ts)

400 MHz NMR CH3-C-CH2CH3

O

(TMS)

CH3-C=O

3.00 2.50 2.00 1.50 1.00 .50 0.0

PPM

Figure 15.1 Conventional representation of the 1H NMR spectrum of butanone�CH3�C = O�CH2CH3�. The corresponding integration superimposed over the peaks permitsan evaluation of the relative areas of the signals. The meaning of the abscissa will be explainedlater on.

always served as a driving force for NMR development and to the numeroustechnical improvements effected since the origin of the technique.

NMR collects information concerning interactions between the nuclei of certainatoms present in the sample when they are submitted to a static magnetic fieldwhich has a very high and constant intensity and exposed to a second oscillatingmagnetic field. The second magnetic field, around 10 000 times weaker than thefirst is produced by a source of electromagnetic radiation in the radiofrequencydomain.

The basic document delivered by these instruments is the NMR spectrum(Figure 15.1), a graph representing signals of resonance. It results from the absorp-tion by the sample of definite frequencies sent by this electromagnetic source. Theorigin of these spectra, which are quite different from optical spectra, can be bestunderstood by consideration of nuclear spins.

� The spectrum of Figure 15.1 is an example of one-dimensional NMR (the intensitiesof the signals not being counted as a second dimension). More sophisticated studies,in two, three and four dimensions enable a more precise localization of the position ofall of the atoms in the molecule studied. This chapter only describes one-dimensionalNMR (1D-NMR), for samples in solution.

15.2 Spin/magnetic field interaction for a nucleus

All atomic nuclei – as well as each particle – are characterized by a number ofintrinsic parameters, spin �I being one of them. This vector quantity introducedby quantum mechanics is used to explain the behaviour of atoms in media wherethere is a preferential direction. A magnetic field creates just such an orientation

15.2 SPIN/MAGNETIC FIELD INTERACTION FOR A NUCLEUS 329

for all atoms within this field. The spin of the nucleus has the same dimensions (Js) as the kinetic moment �L of classic mechanics. The norm of the spin varies fromone nucleus to another because it is defined from the spin quantum number I ,a characteristic of each nucleus considered, whose value can be zero or a positivemultiple of 1/2.

An isolated nucleus with a non-zero spin number behaves like a small magnetwith a magnetic moment �� JT−1� such that:

�� = � · �I (15.1)

This nuclear magnetic moment �� is represented by a vector co-linear to �I(Figure 15.2), and has the same or the opposite direction, according to the signof � the gyromagnetic ratio (also called the gyromagnetic constant).

If an isolated nucleus with a non-zero spin number, which can be comparedto a kind of microscopic magnetic needle, is submitted to a magnetic field�B0 which makes an angle � with the spin vector, an interactive couplingoccurs between �B0 and ��; this modifies the potential energy E of thenucleus.

If ��Z represents the projection of �� on the z-axis, which, by convention, isoriented as �B0, then the energy of the interaction (also called the Hamiltonian) is:

E = −�� · �B0 or E = −� cos��B0 or, finally E = −�z · B0 (15.2)

According to quantum mechanics, �z, for a nucleus, can only have 2I + 1different values. This means that in a magnetic field �B0, the potential energy Ecan also only take 2I + 1 values. The same goes for angle �. The quantification

Z

θB0

I

μzμ

μO

N

S

S

Nproton

Figure 15.2 Basic NMR vectors. When a spinning nucleus is placed in a magnetic field, thenuclear magnet experiences a torque which tends to align it with the external field. In theconventional NMR coordinate system, the external magnetic field is along the z-axis.


of �z are given by the magnetic spin number m which can takes the values (inh/2 units) expressed by the following series:

m = −I−I + 1 � � � I − 1 I

By using relations 15.1 and 15.2, the 2I + 1 allowed energy values are given by thefollowing relations:

E = −� · m · B0 (15.3)

For I = 1/2, the two possible values of E (in joules, and subscripted as � and )correspond to m = +1/2 and m = −1/2. They are given as follows:

E1�orE�� = −�1

2

h

2B0 and E2�orE � = +�

1

2

h

2B0

This splitting in several energy levels recalls the Zeeman effect (cf. Chapter 14)which concerns the separation of electronic states in a magnetic field. It is some-times referred to in NMR as the Zeeman nuclear separation.

The quantification of the spin vector projection along the z-axis has for effectthat �I traces the surface of a cone of revolution with an angle between theaxis and atom that can be calculated if �� and ��Z are known. This precessionmovement, around an axis parallel to that of the magnetic field (Figures 15.3and 15.5a) is characterized by a frequency which increases with the fieldintensity.

ZZ

Y

X

Z

Y

X

Z

Y

X

Z

OS

μ

μ

μμz

μz

N

without magnetic field with magnetic field

B0

B0

spin up

spin down

Figure 15.3 Effect of a magnetic field upon a nucleus of spin number 1/2 for an atom in acompound in solution. If the nucleus is in the upper part of the sample tube, i.e. not submittedto the external magnetic field, �� has no preferential orientation with time. Alternatively, whenthe nucleus is in the strong magnetic field of the central section, it lines up, precessing in the

direction of the applied field. The projection of �� is in the same or the opposite direction to �B0.Unfortunately, here and next figures the dynamic concepts of NMR spectroscopy are difficultto understand whith static diagrams.

15.4 BLOCH THEORY FOR A NUCLEUS OF SPIN NUMBER I = 1/2 331

� To give a concrete idea of nuclear spin, allusion is often made to the movementof a spinning top rotating around its axis, which makes at a given instant, an angle� with respect to the direction of the Earth’s gravitational field. The spinning topdescribes a gyroscopic movement about this direction which arises from the combina-tion of its movement of rotation about its own axis and coupling with the gravitationalvector. As friction slows down the rotation, the angle � will increase continually. Incontrast to the principle of the spinning top, for a nucleus in a vacuum, the angle ismaintained with time, whatever the value of the applied field, because the values ofthe magnetic moment and of its projection are quantized. The rotational axis of thespinning nucleus cannot be orientated parallel, or anti-parallel (although these termsare used for nuclei) with the direction of the applied field �B0. Therefore, for a nucleuswith a spin number I =1/2, calculation leads to the only angles permitted for �I withrespect to z-axis which are approximately 55 � and 125 �. This takes into account thevalue of the spin total angular momentum �

√I(I+ 1)), and that of the intrinsic angular

momentum (I). The angle of 54.74 �, used in certain NMR experiments is called the‘magic angle’.

15.3 Nuclei that can be studied by NMR

In a nuclide represented by AZX, the nucleus will have a non-zero spin number

I , if the number of protons Z and the number of neutrons A, are notboth even numbers. 1

1H 136C 19

9F 3115P have, for example, a spin number I =

1/2 while I = 1 for 21H (deuterium D) or 14

7N. All these nuclei will givean NMR signal. Alternatively, the nuclei 12

6C 42He 16

8O 2814Si 32

16S which have aspin number of zero, cannot be studied by NMR. In fact, more than halfof the stable nuclei known (at least one isotope per element) leads to anNMR signal although the sensitivity varies enormously depending upon thenucleus.

Hence, the protons (the common name for 1H), or 19F, are easier to detect than13C, which is much less sensitive and also for the reason that it represents only 1per cent of elemental carbon.

15.4 Bloch theory for a nucleus of spin number I = 1/2

At a macroscopic scale, even the smallest quantity of a compound is composedof a gigantic number of individual molecules. The number of nuclei beingso high, the NMR signal reflect their statistical behaviour, as in opticalspectroscopy.

Let us consider a collection of identical nuclei whose spin number is I = 1/2.In the absence of an external magnetic field, the individual spin vectors will berandomly oriented and vary constantly with time. From an energy point of view,these nuclei form a population that is considered a degenerated state (Figure 15.3).


E (μeV)

0 1.4 4.7 7 9.3 Tesla

60 200 300 400 MHz(for the proton)

ΔE

ΔE

–1

0.13

0.410.620.82

1

E1

E2

E2 (Eβ)m = –1/2

E1 (Eα)m = +1/2

B0

B0

N

S

S

S

NZ

o

N

Figure 15.4 Representation of the energy split for a nucleus with a spin number I = 1/2 placedinto a magnetic field. The parallel alignment �E1� is slightly lower in energy than the antiparallel

one �E2�. The four values chosen for the field �B0 correspond, for the proton, as it will be

see later, to commercial instruments of 60, 200, 300 and 400 MHz respectively. �B0 representsthe magnetic field strength, measured in Tesla (T). The common values are above 1 T. Forcomparison, the Earth’s magnetic field is approximately 5 × 10−5 T.

When these nuclei are placed in a strong external magnetic field �B0 (OZ orienta-tion) an interaction will occurs between each individual nuclear magnetic vectorand this field.

There appears therefore two groups of nuclei according to the direction of theirspin vector along the z-axis, whose energies correspond to low energy state E1 andto high energy state E2, as previously defined (Figure 15.4). These orientations arecalled ‘spin up’ (magnet image N-S-N-S) and ‘spin down’ (N-N-S-S).

The difference in energy �E between the two states is:

�E = E2 − E1 = �h

2B0 (15.4)

�E is proportional to the field �B0 (Figure 15.4). Thus, for the proton �1H�, ifB0 = 1�4T, the difference in energy is very small: 3�95 × 10−26 J or 2�47 × 10−7 eV.The ratio �E2 −E1�/B0, depends only upon the value for �, for the nucleus beingstudied (Table 15.1).

Table 15.1 Values of � for the most commonly studied nuclei in NMR

Nuclei N ��rad · s−1 · T−1� Sensitivity

1H 2�6752 × 108 119F 2�5181 × 108 0.8331P 1�084 × 108 6�6 × 10−2

13C 0�67283 × 108 1�8 × 10−4

15.5 LARMOR FREQUENCY 333

μ

μ

μ

(a)

μ

μμ

B0 B0OO

Z Z(b)

Y

ZM0

XO

x

xy

y

Figure 15.5 Precession and magnetization. (a) A snapshot illustrating the precession move-ment of the spin vector of five independent nuclei in a magnetic field; (b) The macroscopicmagnetization vector which results from the individual orientations of a large number of nuclei.If B0 = 1�5T, there are less than 10 spin-up more than spin-down per million 1H nuclei. Thevalues of this very weak net magnetization depends on the excess of population E1 versus E2.By convention the external magnetic field and the net magnetization vector at equilibrium areboth along the z-axis.

The population of nuclei located in energy state E2, is slightly less numerousthan that in the more stable state E1. Expression 15.5 calculates the ratio of thesetwo populations (Boltzmann distribution equilibrium).

R = N2

N1

= exp

[−�E

kT

](15.5)

(for 1HR = 0�999964 if T = 300K and B0 = 5�3T where k = 1�38 ×10−23 J K−1 at−1).

As a result, it is only the slight excess in population E1 which is responsible forthe NMR signal. By increasing the value of the magnetic strength of the magnet,the difference �E will be greater and thus sensitivity will increase since the signalis proportional to the populations difference.

On a graphic representation, the weak magnetization of the sample solutionis accounted for by using the vector �M0, which is the vector sum of all of theindividual vectors �� (Figure 15.5). At equilibrium, this vector lies along the direc-tion of the applied magnetic field �B0 and is called the equilibrium magnetizationor net magnetization. �M0 is used to describe pulsed NMR, and to explain theappearance of signals when nuclei enter resonance. �M0 is an entity to which thelaws of electromagnetism can be applied.

15.5 Larmor frequency

From an analytical point of view, a nuclide can be identified if �E, in a field�B0, could be measured (assuming I = 1/2), by knowledge of the gyromagnetic


constant �. As in optical spectroscopy, this difference in energy can be determinedunder conditions where species can pass between one state and the other, byabsorption or emission of a photon.

A basic experiment consist of irradiating the nuclei present in a magneticfield with a source of electromagnetic radiation of variable frequency � with apropagation direction perpendicular to the external field. Absorption will occur if:

h� = �E = E2 − E1 (15.6)

The energy of this photon must exactly match the energy difference between thetwo states. Expression 15.4 leads to the fundamental relation of resonance (15.7):

� = �

2B0 (15.7)

This important and general expression, irrespective of the value of I , gives thefrequency Larmor frequency. It links the magnetic field in which the nuclei beingstudied are located and the frequency of electromagnetic radiation that inducesresonance, hence a signal in the spectrum when the lower energy nuclei spin-flipto the higher state (Table 15.1).

The radiofrequency which induces the exchange between the two levels is equalto the Larmor frequency at which the spin vector rotates about the averagedirection of the z-axis. Larmor, an Irish physicist whose work preceded thatof NMR has shown, by an independent reasoning that �, the angular rotationfrequency of the spin vector about the z-axis, has a value of:

� = � �B0

This is the Larmor equation. Since � = 2�, this expression is equivalent toEquation 15.7. The two approaches are different: one leads to the frequency ofthe quanta which separates both energy states and the other to the mechanicalprecession frequency. These two frequencies have the same value.

The Larmor frequency of a given nucleus increases with �B0. It is situated inthe microwave region of the electromagnetic spectrum and varies, for a field of1 T, from 42.5774 MHz for the hydrogen 1H nucleus (proton) to 0.7292 MHzfor gold 197

79Au (Table 15.2). The instruments are specifically designed for thefrequency at which protons resonate, even if they are of able to study othernuclei.

Table 15.2 Values in MHz of some resonance frequencies for �B0 = 1T

Nuclei 1H 19F 31P 13C 15N

Frequency � 42.58 40.06 17.24 9.71 4.32

15.6 PULSED NMR 335

Sig

nal i

nten

sity

(ar

b. u

nits

)

Magnetic field ( Tesla )

0.1 0.3 0.5 0.7 0.9

11B

63Cu

1H

65Cu

23Na

27Al 29Si 2H 17O

Figure 15.6 NMR spectrum of a water sample placed in a borosilicate glass container, observedat a frequency of 5 MHz (the field is expressed in gauss; Varian document). There are nocommercial instruments of this type because NMR is not sensitive enough to solve many of theproblems encountered in elemental analysis.

The construction of experimental multi-nuclei instruments was initiated fromthese principles. These instruments can sweep over a wide range of the field whilemaintaining a fixed radiofrequency. This leads to a qualitative screening of theeasiest elements to detect within the sample through their characteristic resonance(Table 15.2 and Figure 15.6).

15.6 Pulsed NMR

�M0 that is shrouded in the strong magnetic field �B0 is too weak to be measured.So, to get a signal, resonance of the nuclei is obtained by superimposing upon �B0,in the probe area, a weak oscillating field �B1 which originates from a coil that isfed with alternating current radiofrequency.

To understand the interaction of the nucleus with the field �B1 in the laboratoryframe of reference, it is considered as resulting from the composition of twovectors rotating in opposite directions (clockwise and counter clockwise) in thexy-plane with the same angular velocity (Figure 15.7). If the frame of referencerotates with the precession frequency, the vector component that also rotatesclockwise in the laboratory frame of reference will appear stationary. The secondvector component that rotates counter clockwise is moving around the z-axis farfrom the resonance frequency of the spins. It can be ignored. Only the vectorturning in the same direction as the precesion movement can interact with thenucleus. As transverse magnetization rotates about the z-axis, it will induce acurrent in a coil of wire located in the xy-plane.

For �B1 to be suitably aligned, the propagation axis of the radiofrequency needs tobe perpendicular to the z-axis (Figure 15.8). The transfer of energy from the source


μ

ZZ

X

Y

OO

B0

XY

B1

b2

b1

Figure 15.7 Representation of magnetic field �B1. In all points of the plane xy the magnetic

component of the wave can be dissociated into two half vectors �b1 and �b2 rotating in phase

with opposite velocities. Here, only �b2 can interact with the nuclei of population E2.

xy

ZZ

Z

ZZ

O XYO XY

M0

M0

M0

M0

M0

MZ

α

Z

O

O

XY

Figure 15.8 Deviation of �M0 with irradiation and relaxation of the transverse and longitudinalrelaxations of the system following resonance. Schematic representation in which the individualvectors form a spin packet resulting from the non-equilibrium of the populations are shown

(laboratory frame of reference). �B1 has a double action, flipping the nuclei and packing themin phase. An observer situated in a rotating frame at the precession frequency, would see the

magnetization vector tilted by an angle �. Relaxation of �M0 to its original position. If �MZ = 0,the spin system is saturated. As transverse magnetization rotates about the z-axis, it will inducea current in a coil of wire located around the x-axis. Plotting current as a function of time givesa sine wave.

15.6 PULSED NMR 337

to the nuclei occurs when the radiofrequency of the source and the frequency ofprecession are identical. Under these conditions the spin of some nuclei adoptsthe second alignment allowed (in the case where I = 1/2). Nuclei in energy stateE1 pass to energy state E2: in this way, the populations are modified. Saturationis attained when they become equal.

Before irradiation, the individual vectors �� are out of phase with respect toeach other, which is represented by the vector �M0, aligned in the direction OZ(Figure 15.5). As the resonance condition is reached, all the individual vectors packtogether and rotate in phase with �B1. Thus, the direction of �M0 changes by an angle� (relative to z-axis), which can be controlled from 0 to , by adjusting the timeand the intensity of the applied radiation. Figure 15.8 illustrates this phenomenonwith several individual vectors which join together. It is for this reason that �M0

acquires a �MXY component in the horizontal plane which is maximum when� = /2 and conserves a variable component �MZ in the z-axis direction (exceptwhen � = /2). The frequency of the rotation of the magnetization vector isalways equal to that of the precession movement. When the irradiation ceases thesystem returns progressively to the initial state of equilibrium. A coil detects thecomponent in the y-direction (Figure 15.8).

What happens in the probe of the apparatus? A common interpretation suggestsimagining an external observer linked to a rotating frame about the z-axis at thefrequency of precession of the concerned nuclei (Figure 15.8). For example, let usassume the case of a single precession frequency. When the radiofrequency hasthis particular value, the nuclei seem, to the observer, to feel only the effects of therotating component of the field (i.e. perpendicular to z-axis). The magnetizationvector deviates until an angle �. After the pulse the individual magnetic momentslose their phase coherence through interaction with the spins of the neighbouringnuclei, faster than they can re-align themselves according to the Boltzmann distri-bution function which described the populations before the pulse. Thus, �M0 losesits xy-plane component, without having returned to its initial value in the OZdirection, which can take a longer period of time.

� The actual process for obtaining the whole range of frequencies by computationdid not exist when the first generation of NMR machines were built. In the earliestNMR instruments, the former approach consisted of obtaining resonance by sligthlymodifying �B0 using a coil wrapped around the pole piece of the magnet (Figure 15.9).Because these instruments used to sweep the magnetic field, they operated at asingle frequency (CW-NMR). The spectrum was nevertheless recorded in Hz sincethe Larmor equation corralates field with frequency. This form of absorption NMR canalso be performed with a constant magnetic field and a frequency which is varied.This process for finding the signal is similar to the sequential method of recordingoptical spectra, or even in daily life, when seeking an FM radio station on an analoguereceiver transistor.

In this mode of acquisition, the quality of the spectrum depends on a small fractionof the total recording time. Fourier transform spectrometers make much better useof the recording time.


Oscillator (field B1 ) Detection

Adjustment of field B0

B1B0

(Radiofrequency)

Y

Spectrum

1951

Signal

X

Z

HO CH2CH3

Figure 15.9 CW-NMR. Arrangement of the different coils around the probe between the poles ofthe magnet. Signal is detected along x or y axes. Right, an historic recording (1951) of the protonspectrum of ethanol. The three signals correspond to the six hydrogen atoms of CH3CH2 andOH. This will be better understood after reading Section 15.8.

Technically speaking, the sample is irradiated for a few microseconds withan intense pulse, which is a means of exposing the sample to all frequenciesincluded in the domain to be sampled. This can be compared to a flash ofwhite light (comparing a polychromatic light with respect to a monochromaticsource). For example, when working at 300 MHz, in order to irradiate all of theprotons whatever their environment, a frequenciy range covering at least 6000 Hzis required. Under these conditions a small fraction of each type of proton (butnot all the nuclei), will absorb the resonance frequency.

To find a schematic representation for a compound absorbing tens of frequen-cies is obviously impossible. In such cases, �M0 can be dissociated into many vectors,each of which precesses around the field with its own frequency (Figure 15.8,for a simplified situation). During the return to equilibrium, which can takeseveral seconds, the instrument records a complex signal due to the combinationof the different precession frequencies present, of which the intensity decreasesexponentially with time (Figure 15.10).

This damped interferogram is called free induction decay or FID. The signalcorresponds at each instant to an overall numerical value which informs on thefrequencies of the nuclei that have attained resonance at that particular instant.These values can be transformed by Fourier calculations that converts the signalfrom the time domain into a classically spectrum of the frequency domain.

This pulsed wave technique, is a simultaneous method in the sense that theapparatus acquires, at each instant, information concerning all of the frequenciespresent. The major developments of current NMR result from the generalizationof this procedure which permits the study of less sensitive nuclei, such as 13C.

15.7 THE PROCESSES OF NUCLEAR RELAXATION 339

Figure 15.10 Interferogram of fluroacetone obtained with a pulsed wave NMR instrument. Thesignal I = f �t�, after conversion to a classic spectrum I = f �� by Fourier transform, is that ofthe spectrum shown in Figure 15.18. The interferogram, recorded over of a few seconds can beaccumulated many times to improve the signal/background noise ratio. The computer does notrecord a continuous FID, but a FID that is sampled at a constant interval.

15.7 The processes of nuclear relaxation

After the pulse of radiofrequency, �M0 will regain its equilibrium value aftera relaxation time which is depending upon the element and the medium(Figure 15.11). This relaxation period depends on both the reconstitution of thepopulations to their initial state (time constant T1), named longitudinal relaxation(spin lattice relaxation) and on the loss of phase coherence (time constant T2),called transverse relaxation (spin–spin interactions). Each of the spin packets isexperiencing a slightly different magnetic field and rotates at its own Larmorfrequency. In solution, T1 is never longer than a few seconds (for 1H), while it

Inte

nsity

Time

MXY

MZ

T1T2

Spin/spin relaxation

Spin/lattice relaxationSpin/lattice relaxation

M0MXY(0)

0.63 M0

0.37 MXY(0)MXY = MXY(0)Exp(–t/T2)

Z

X

Y

MXYMz = M0 Exp[1 – Exp(–t/T1)]

Figure 15.11 The two processes of nuclear relaxation. Evolution over time of spin–spin andspin/lattice relaxation. T1 is defined as the time required to change the z-component of magne-tization by a factor of e. The greater the rigidity of the medium, the smaller T2 will be. T2 isalways less than or equal to T1. The net magnetization in the xy-plane goes to zero and then

the longitudinal magnetization grows in until to get �M0 along the z-axis.


can be as long as several hours with solids. These two components of �M0 musttherefore be dissociated. Knowledge of the lifetimes of T1 and T2 yields veryuseful information on the structure of the samples analysed. T1 decreases whenthe viscosity of the medium increases, which causes signal broadening. Changesin T2 also has an effect upon the width of signals. A neat liquid compoundleads to broader signals than they would be if the compound was in a dilutesolution.

15.8 Chemical shift

So far as NMR is concerned, molecules present in dilute solutions form inde-pendent entities that do not interact noticeably between themselves. Alternatively,within a given molecule, the electronic and steric environment of each nucleuscreates a very weak local magnetic field which shields it more or less from theaction of the external field �B0. Each atom has a particular environment – at leastif there are no specific elements of symmetry in the molecule. According to theLarmor equation, these very weak local variations in the intensity of the field willaffect the frequency of resonance as compared to what would be seen in a vacuum.This effect is called shielding or deshielding of the nuclei.

This observation is the basis of the principal exploitation of NMR: rather thanobserving all of the nuclei present, spread over a wide range of frequencies (severaltens of megahertz), the study focuses on a single type of nucleus at a time. In otherwords the technique zooms over a very narrow range of frequencies (for example1000 Hz) in order to record the different signals which result from specificities ofeach compound (Figure 15.1). This screening effect is quantified by the shieldingconstant � which appears in equation 15.8 linking the effective field Beff whichreaches the nucleus with the external field B0:

Beff = B0�1 − �� (15.8)

All variations in � affect the resonant frequency of the corresponding nucleus.This phenomenon is called a chemical shift. As many chemical shifts are observedas there are molecules containing different shielding constants � . Consequentlylarge molecules lead to complex spectra as a result of their numerous � values. Fora nucleus i for which I = 1/2, the Larmor equation becomes, on the introductionof the effective field Beff :

�i =�

2B0�1 − �i� (15.9)

Concerning the proton 1H, expression 15.9 leads to a difference of 1 Hz for theresonance frequency when the surrounding field varies of 2�3 × 10−8 T, while avariation of 10−4 T (1 gauss) induces a shift of 4258 Hz. For this reason the setting

15.9 MEASURING THE CHEMICAL SHIFT 341

of the magnet must be perfectly controlled in order to maintain the stability ofthe field B0 in the NMR instrument. Thus, the temperature has to be controlledto within a 1/100th of a degree. Furthermore, the sample is rotated in a tubewith very thin walls to reduce the heterogeneity of the field. Considering theseconstraints, the construction of mobile NMR instruments is a real achievement(Figure 15.33).

15.9 Measuring the chemical shift

According to the Larmor equation, the slightest variation in the field has reper-cussions on the resonance frequencies. Thus, it would be inadvisable to try tocompare spectra or identify compounds using the absolute signal frequenciesobtained with different instruments. For this reason the chemical shift is refer-enced by a relative scale ��/�, which is independent of the instrument. That iswhy a compound acting as an internal standard is used and can therefore serve asa fixed reference, as well as the frequency �app of the instrument. For the nucleusconsidered, the different chemical shifts can then be obtained by dividing thefrequency difference �� between each signal of the compound studied and thatof the standard, by the characteristic frequency �app of the instrument (expres-sion 15.10).

The values obtained are expressed in parts per million (ppm). In order tocalculate the chemical shift �i (ppm) corresponding to a signal of frequency �i

with respect to an internal standard ��ref �, there is no need to know the absolutefrequencies, only �� is necessary.

�i =�i − �ref

�app

· 106 = ��

�app

· 106 (15.10)

The internal standard used for both 1H and 13C NMR is tetramethylsilane(TMS). This inert and volatile compound (boiling point = 27 �C), yields a singlesignal in both 1H NMR (for the 12 equivalent protons) and in 13C NMR (forthe four equivalent carbons). TMS signal is positioned at origin of the � scale(Figure 15.11). Almost all organic compounds have positive values for �, rangingfor 1H from 0 to 15, to 250 for 13C.

� The TMS signal is located on the right-hand of the spectrum, respectingthe convention according to which, in spectroscopy, the energy parameter, posi-tioned along the abscissa, decreases when moving towards the right of thespectrum.

The � scale has enabled the generation of empirical correlation tables basedon the chemical shifts as a function of chemical structure, which can be usedirrespective of the NMR instrument (Tables 15.5 and 15.6 at the end of thischapter). Expression 15.10 shows that if the spectra of the same compound,


Chemical shift (ppm)

CHCl3

Low fields

(Deshielding)

High fields

(Shielding)

TMS

012345678910

CH3

Si CH3

CH3

H3C (TMS)

HF(gas)H2H2O(liq.)HF(liq.)

–4

HBr

HI

–14

Increasing B experienced by nucleus increasing σincreasing ν at fixed B

32

H+(bare proton)

13H(atom)

Figure 15.12 Chemical shifts of certain compounds in proton NMR. Shielding effects recordedwith a fixed frequency instrument.

recorded with two instruments whose fields B0 make a ratio between them of k arecompared, then the frequencies of the homologous signals for the two spectra willbe in this same ratio k, the values of � remaining the same. However, these tablesare not always sufficient to make a correct attribution of the signals. Softwareprograms have been developed to help in this regard.

15.10 Shielding and deshielding of the nuclei

The more marked the screening effect, the more the nuclei are said to be shielded:in order to obtain resonance the value of the field �B0 must be increased, at leastwhen referring to a continuous wave instrument operating at fixed frequency.Signals situated to the right of the spectrum are said to be resonant at high field andby contrast signals observed to the left of the spectrum correspond to deshieldednuclei and are said to be resonant at low field (Figure 15.12).

15.11 Factors influencing chemical shifts

Examination of a large number of NMR spectra allows to highlight the factorsthat are responsible for predictable and cumulative effects on the chemical shifts.

15.11.1 Effects of substitution and hybridization

The simple replacement of a hydrogen atom by a carbon-containing group Rproduces a deshielding of the remaining protons. This substituent chemical shiftreaches 0.6 ppm when comparing RCH3 to CHR3. This effect can attain 40 ppmfor 13C NMR. The state of hybridization of the carbon atoms greatly influencesalso the position of the signals.

15.11 FACTORS INFLUENCING CHEMICAL SHIFTS 343

These anisotropic variations are due to the chemical bonds, that is, to the non-homogeneous electronic distribution around bonded atoms, to which can be addedthe effect of unimportant magnetic fields induced by electron circulation. Ethylenicprotons are therefore deshielded as they are positioned in an electron-poor plane.Inversely, acetylenic protons are shielded, because they are located in the axis of theC–C bond and so, plunged into an electron-rich environment. Aromatic protonsare displaced towards lower fields because, as well as the anisotropic effect, a localfield produced by the movement of the aromatic electrons or the ‘ring current,’is superimposed to the main magnetic field (Figure 15.13).

15.11.2 Resonance and inductive effects

The chemical shifts of organic compounds are sensitive to the delocalization ofelectrons bonding. Particularely, the existence of mesomeric forms provokes largeshifts of the signals (Figure 15.14).

Thus, it is comprehensible that the electronic effects which modify the polarityof the bonds have an influence upon the chemical shifts. Table 15.3 illustratesthe effect of electronegativity upon the position of the methyl signal in thehalomethane series CH3-X where the chemical shift of the carbon atom signalincreases with the electronegativity of the halogen X.

H

C

C

H

C CH

H

H

HC

C CC

C CH

H

HH

H

H

σB0

σB0σB0

B0B0

σB0

Figure 15.13 Anisotropic effects and induced local fields. The presence of -bonding can betranslated as zones of either a �+� shielding or a �−� deshielding effect. The ethylenic protonsare at the outside of a kind of double cone of protection while the aromatic protons undergothe effect of the electrons moving in two parallel circular clouds.

+ – + –O

R

RC O

R

ROC O

R

ROCO

R

RC

a ketone an ester(205 ppm) (165 ppm)

Figure 15.14 Effects on NMR signals of the resonance effect in mesomeric forms of a carbonyl.If the carbonyl of a ketone is compared with that of an ester, then it should be noted that forthe ketone, the more electropositive of the two, the carbon has less protection than the ester.In 13C NMR the carbonyl signal for a ketone is around 205 ppm while for an ester it is around165 ppm.


Table 15.3 Influence of the electronegativity �∗ of a halogen on � (TMS ref.)

CH3F�� = 4� CH3Cl�� = 3�2� CH3Br�� = 3� CH3l�� = 2�6�

�H (ppm) 4�5 3 2�7 1�3�C (ppm) 75 30 10 −30

∗ electronegativity � in eV according to the pauling scale

15.11.3 Other effects (solvents, hydrogen bonding and matrix)

1H NMR spectra of organic compounds are usually obtained in solvents notcontaining hydrogen atoms. The solvent, far more abundant than the soluteof which the concentration is only of several percent, leads to associations ofwhich the stability depends upon the respective polarities. Consequently, thesample concentration and solvent used must be provided with the correlationtables.

The most widely used solvent is deuterated chloroform �CDCl3� which issufficiently polar to dissolve the majority of organic compounds. Also used areacetone-d6�C3D6O�, methanol-d4�CD3OD, pyridine-d5�C5D5N� or heavy water�D2O�.

� In 1H NMR, the position of the chloroform signal in mixtures chloroform/toluenevaries from 7.23 ppm (90 per cent chloroform/10 per cent toluene v/v.) to 5.86 ppm(10 per cent chloroform/90 per cent toluene). This shift towards a higher field, fortoluene-rich mixtures rich is explained by the presence of complexes causing theproton of chloroform to be located in the protecting zone of toluene’s aromaticnuclei.

When the studied compounds have labile hydrogen atoms, D ↔ H exchangescan occur in certain solvents. These exchanges will cause alterations to the intensityand position of the relevant signals. Likewise, hydrogen bonding is able to modifythe electronic environment of some protons making their chemical shift sometimesdifficult to predict.

Finally, interactions between neighbouring molecules and also the effect ofviscosity will alter the resolution of the spectrum through the spin/lattice relax-ation time.

15.12 Hyperfine structure – spin–spin coupling

As a general rule, NMR spectra contain more signals than there are nuclei withdifferent chemical shifts. This phenomenon is due to the external magnetic fieldwhich influences all of the atoms of the sample compound, causing an alignmentof all nuclear spin and that the orientation taken in the magnetic field by one

15.13 HETERONUCLEAR COUPLING 345

nucleus affects the neighbouring nuclei, through valence electrons. If the distancebetween non-equivalent nuclei is less than or equal to three bond lengths, thiseffect called spin–spin coupling or J coupling is observable. Homonuclear coupling(between nuclei of the same type) or heteronuclear coupling (between nuclei ofdifferent types, as 1H/13C)) gives rise to small shifts in the signal. This hyperfinestructure of the spectrum brings additional information about the compoundwhich is studied. Homonuclear coupling between protons is quite frequent.The presence of 13C 31P and 19F leads also to heteronuclear couplings with theprotons.

� This phenomenon must not be confused with the interaction through distancebetween two nuclei which exchange their magnetization because the structure of themolecule is such that they are in close proximity in space, although a great numberof bonds separate them. This is the Nuclear Overhauser effect which manifests itselfby modifications in signal intensities.

15.13 Heteronuclear coupling

15.13.1 Hydrogen fluoride: a typical heteronuclear coupling

Hydrogen fluoride (HF) is a simple molecule that allows the observation ofa spin–spin heteronuclear coupling between the two atoms that are linked bya covalent bond. When the 1H spectrum of this compound is examined, twosignals of equal intensity are observed though the molecule itself contains onlyone hydrogen atom (Figure 15.15). The reason for this is the following: whena sample of this compound is placed in the probe of the instrument, thatis equivalent to insert a very large number of individual hydrogen fluoridemolecules into the magnetic field �B0. Knowing that both H and F have the spinnumber I = 1/2, the molecules are distributed at thermal equilibrium into fourpopulations E1 to E4, that correspond to the following spin combinationsgiven on Figure 15.15.

If there was no interaction between the H and F nuclei, the populations E1

and E2 on one side and E3 and E4 on the other, would have the same energyand consequently in 1H NMR, only a single signal would be seen (Figure 15.16).However the reality is different as an interaction exists between H and F. With

H—F H—FH—FB0

1 2 3 4

E1 E2 E3 E4

H—F

Figure 15.15 HF sample in 1H NMR – the four populations in the magnetic field �B0.


J/2 J/2

J = 615 Hz

ν1ν

ν

ν2

B0

E

0

+ J/4

+ J/4

– J/4

– J/4

H—F

Hα Fβ

Hα Fα

Hβ Fα

Hβ Fβ

ν2ν1

E3

E4

E1

E2

1

2

3

4

Figure 15.16 Coupling diagram for the HF molecule in 1H NMR. Hypothetical comparison ofthe situation in which there is no coupling with the fluorine atom and the real situation. Thevalues for �1 and �2 differ in length by J Hz.

respect to the situation in which no coupling arises, a theoretical developmentleads to the conclusion that the two populations E1 and E2 correspond now totwo different energy states: it follows that there will be a spliting-up of the peakas supposed previously. The energy required to go from E2 to E3 is not the sameas from E1 to E4. The spin orientation taken by the fluorine atom has an effecton the transition energy observed in 1H NMR. The spectrum of this compoundwill therefore contain two peaks corresponding to the transitions situated onFigure 15.16.

The coupling constants, expressed in hertz, are available from the NMR spectrum.They are designated by the letter J with an index giving the name and the numberof bonds which separate these atoms. If we consider the case of HF, the couplingconstant can be written:

1JFH = 615Hz

The spin orientation of the fluorine atom, which has a resonance frequencyvery far from that of the proton, will not be disturbed by the resonance occuringin protons : in a field of 2.35 T 1H resonates at 100 MHz while 19F resonates at94 MHz. The two peaks of the 1H signal are separated by 615 Hz, irrespective ofthe intensity of B0. The 19F NMR spectrum for this molecule would lead to asimilar spectrum. Two peaks would be observed separated by 615 Hz, due thistime, to the coupling with the proton following one or other of the orientationchosen.

When the number of bonds separating the atoms concerned increases, the spin–spin couplings weaken very quickly, assuming that there are no multiple bonds(double or triple) which could propagate the spin effect through the -bondelectrons.

15.14 HOMONUCLEAR COUPLING 347

1JCD = 32 Hz

80 78PPM

76 74

Figure 15.17 13C Spectrum in CDCl3 showing the coupling 1JCD. The three signals of thisspectrum are caused by the heteronuclear coupling between the 13C and the atom of deuterium2H (or D), (coupling 1JCD = 32Hz). Since the deuterium has a spin number I = 1, there arethree possibilities for m: −10+1, which leads to the triplet. The three components are ofequal intensity as there is only a single atom of deuterium. This triplet is present on almost all13C spectra, in superimposition, when this solvent is used.

15.13.2 Heteronuclear coupling in organic chemistry

The presence in a molecule of atoms such as 13C 1H or 19F which possess a spinnumber of 1/2, is at the origin of numerous heteronuclear couplings, exploitedfor their structural information (Figures 15.17 and 15.18).

15.14 Homonuclear coupling

Signal splitting, as studied in the case of hydrogen fluoride, is often encounteredin organic compounds with adjacent hydrogen atoms if their chemical shifts aredifferent.

15.14.1 Weakly coupled systems

Nuclei are said to be weakly coupled when the coupling constants are muchsmaller than the differences in chemical shifts of the nuclei concerned (afterconversion in Hz). The ethyl group of butanone (Figure 15.1) illustrates thissituation. These five protons – 3 and 2, weakly coupled give rise to threepeaks (a triplet) towards 1.1 ppm and to four peaks (a quadruplet) towards2.5 ppm.

The origin of these peaks in the spectum can be ascribed by their chemical shifts(Table 15.5). The triplet is due to the CH3 and the quadruplet to the neighbouring


ppm

(ppm)

(ppm)

1952

.83

1905

.29

899.

09

899.

09

2.30 2.20

012345

–225.8 –225.9 –226.0 –226.1 –226.2

894.

99

894.

99

H

CH

H

C

O

C

H

F

H

“Proton spectrum”

“Fluorine spectrum”

Figure 15.18 NMR spectra of monofluoroacetone. An example of heteronuclear coupling.Above, the 1H NMR spectrum. The presence of the fluorine atom leads to a doublet for themethyl group �3J = 4�1Hz� as well as for the CH2�

2J = 47�5Hz�. Below, spectrum of 19F . Thesingle fluorine atom of this molecule leads to a triplet with the CH2 group and a quadrupletwith the methyl (explanation in next section). The resulting signal is therefore a triplet ofquadruplets. With the aid of table 15.4 the coupling constants can be calculated and comparedfor the two spectra (the scale for the chemical shifts is positioned with respect to FSiCl3.

CH2. The relative intensities of the components, within each of these multipletscan be deduced by the laws of statistics (Figure 15.19 and Table 15.4).

As a general rule for weak couplings, if n nuclei (spin number I), are placedin the same magnetic environment, influencing in an identical manner one orseveral adjacent nuclei, then the signals observed for the latter will be formed of2nI + 1 peaks regularly spaced – i.e. �n+ 1� signals in the case where I = 1/2. TheT1 and T2 values of all the spins must be equal. The peak intensities in a multipletwill follow the same pattern found in each row of Pascal’s triangle (Table 15.4).However, if a group of protons is submitted to the effect of neighbouring nucleifor which the chemical shifts and the coupling constants are different, the previous


two protons of the methylene group (-CH2-) three protons of the methyl group (-CH3)

the two protons of the CH2 groupare influenced by the three protonsof the CH3 group and vice versa.Energy Increasing from right to left

Energy Increasing from right to left

1 2 3

1 2 3

1 2

1 2

1 2

1 21 2 3

1 2 3

1 2 3

1 2 3 1 2 31 2 3

triplet

B0

quartet

Figure 15.19 Representation of the different spin states for the five protons of an ethyl group. Inthe same row are found the spin states which produce the same effect on neighbouring nuclei.The sample contains a large number of identical molecules, these are distributed across severalpopulations giving each one a statistically weighted signal like the number of states per row ofthis scheme.

Table 15.4 Pascal’s triangle and its application to NMR for I = 1/2

Neighbouring hydrogens Multiplicity Intensity

0 singlet 11 doublet 1 12 triplet 1 2 13 quadruplet 1 3 3 14 quintuplet 1 4 6 4 15 sextuplet 1 5 10 10 5 16 septuplet 1 6 15 20 15 6 1

approximation is no longer applicable: the multiplicity of the signals and theintensity of the peaks cannot be deduced so easily.

� Nomenclature for coupled systems in 1H NMR. Spectral interpretation for amolecule with many hydrogen atoms is easier when sub-groups of signals corre-spond to classic situations. These particular cases are classified by means of anomenclature using the letters of the alphabet, selected with respect to the chemicalshift (Figure 15.20). Protons with the same chemical environment or chemical shiftare called equivalent. If the chemical shifts are too little different, the protons are


δ(ppm)

A B C ... M ... X

0

TMS

CH2

CH3

O

Cl

H

H

H

H3C

A2 X3

A3

AMX

Figure 15.20 NMR nomenclature of spectra. The 1H spectrum of 3-chloro-4-methylpropiophenone is the complex result of the superimposition of the signals of severalindependent yet easily recognized sub-groups.

designated by the first letters of the alphabet (AB, ABC, A2B2, A3), while protons withvery different chemical shifts are designated by letters such as A, M, and X (i.e. AX,AMX, AX3, etc.). Like this, the ethyl group (as ethoxyl), constitutes a system A2 X3;the protons of ethanal represent an AX3 system while a vinyl group will be ABC, AMXor ABX depending upon the example studied.

In 13C NMR, as the coupling constants 1JC-H being of the order of 125 to 200 Hz,there are frequent signal overlappings, which makes the spectrum more difficultto interpret. Technically it is possible to eliminate the entire set of couplings forall of the protons (see Figure 15.21).

4 578

6

3

PPM

140 120 100 80 60 40 20 0

2

1

6

54 2 1

3

87

CH2–CH3

Figure 15.21 Proton decoupled 13C spectrum of ethylbenzene. Each carbon atom gives asingle signal consisting of a singlet. These simpler ‘broad band,’ decoupled spectra yield lessinformation.


15.14.2 Strongly coupled systems

When the ratio ��/J is small the protons become strongly coupled. The intensitiesof the multiplets are then very disturbed. New peaks arise from combinations offrequencies hindering the interpretation of spectra. This is one of the reasons forthe development of instruments operating at higher frequencies �300→750MHz�with supraconducting magnets to obtain the required magnetic fields. Given that�� is proportional to the operating frequency, while J remains constant, the ratio��/J increases and again nuclei appear as weakly coupled (Figure 15.22). Howeverthere are other phenomena that complicate the spectra when the frequency exceeds600 MHz.

AB system. When the difference in resonance frequencies between two protonsis comparable with their coupling constant J , then this system gives rise to atotal of four peaks. This is the simplest strongly coupled system. The signalfor each proton contains two peaks separated by J Hz. However the inten-sities are no longer equal and the chemical shifts, which can no longer beread from the spectrum, must be calculated from the expressions indicated onFigure 15.23.

90 MHzSolvent CDCl3

400 MHzSolvent C6D6O

H

H

HH

O

CO2H

O

CH3

d

c

b

a

8 7,2 ppm

8.10 8.00 7.90 7.80 7.70 7.60 7.40 7.30 7.20 7.107.50

a c b d

PPM

Figure 15.22 Spectrum of the four aromatic protons of aspirin. The figure above reproduces,with a similar scale, aspirin spectrum obtained on two different instruments, one running at90 MHz (solvent CDCl3) and the other at 400 MHz (solvent C3D6O). The sensitivity of NMR

grows as �B3/20 .


νΑ

νΑ

ν0

ν0

νΒ νΑ νΒ

νΑ νΒ

ν0 νΒ νΑ ν0 νΒ

(a)

(c)

(b)

(d)

J J

m

n

n + J = mn + J2

νA – νB = mn νA + νB

2ν0 =

= mnIext

Iint

12

νA = ν0 + mn mn12

νB = ν0 –

Figure 15.23 Characteristics defining an AB system. (a–d) Gradual modification of a two-proton coupled system as the ratio ��/J decreases. Typical appearance and formulae used toanalyse an AB system.

15.15 Spin decoupling and particular pulse sequences

NMR instruments have accommodated numerous advances to facilitate spectralinterpretation. Thus it is possible to cancel the effect of an existing spin-couplingbetween neighbouring nuclei. This spin decoupling technique is based on thestatement that a nucleus in resonance does not always conserve the same spin statewith time. This uninterrupted and fast transfer between different states induces aglobal effect upon the neighbouring nuclei.

In practice, a spin decoupling experiment begins with a record of the spectrumunder normal conditions. Next, decoupling is achieved with the aid of a saturationpulse: a second spectrum is recorded while irradiating at the resonance frequencyof the nucleus (or nuclei) that is (are) to be decoupled (Figure 15.24). This doubleresonance technique is used to identify nuclei which are coupled and which causeinterpretation difficulties in the spectrum, in particular for superimposed signals.

Fourier transform NMR at high fields (B0 = 17�6T for the study of 1H at750 MHz) has considerably extended the potential of this method. This is due toan increase in acquisition speed and rapid computation of spectra.

A variety of experiments based upon particular pulse sequences can be appliedto a sample to produce a specific form of NMR signals. For example, the 90-FIDpulse sequence rotates the net magnetization down into the xy-plane, throughwhich the relaxation times of the nuclei can be determined. Amongst the more

15.15 SPIN DECOUPLING AND PARTICULAR PULSE SEQUENCES 353

(a) (b)

3.0 2.5 2.0 1.5 1.0 .5 3.0 2.5 2.0 1.5 1.0 .5

Figure 15.24 Spin decoupling experiment on butanone. Modification of the 1H spectrum by(a) Irradiation of the CH2 group at 2.47 ppm; (b) Irradiation of the CH3 group (of ethyl) at1.07 ppm, both for comparing with the spectrum of butanone, Figure 15.1. For such a simplecompound such as this, the experiment is only of illustrative interest. On the other hand, adouble resonance experiment would allow the precise determination of the different couplingsin aspirin (Figure 15.22).

classical methods, multidimensional 2-D or 3-D NMR allow the deduction of veryuseful structural information. When analysing bio-polymers such techniques leadto results comparable with those obtained by radiocrystallography, permitting,amongst other things, the representation of molecular conformations in theirnatural medium.

� Magnetic resonance imaging (MRI) Proton NMR can be exploited to obtainimages of all objects containing hydrogen atoms, from living organisms to geologicalstrata. This important development of NMR has been successfully applied to medicalanalysis under the name of MRI, a form of non-invasive physical observation, withoutpenetration, adapted to soft tissues. The volume to be examined must be placedin a magnetic field, which requires the manufacture of very large supraconductingmagnets for total body instruments. Proton signals are the easiest to observe sincebiological tissues contain around 90 per cent water (an individual of 70 kg comprises50 kg of water compared to 13 kg of carbon). In other cases the signal of the CH2groups, present in lipids, are monitored. The final image is a cartographic presentationof the intensity distribution of the same type of proton signal. The contrast in theimage is due to the variations in relaxation times for the protons of the selected plane.Amongst the specific technical complexities is the focusing, or spatial selectivity,needed to obtain a spectrum of a quasi-punctual volume within an object. ‘Slices’ ofthe patient are imaged as a matrix of small volumes of tissue (voxels) producing anindividual signal. These ‘slices’ can then be reconstructed to provide images in anyplane (Figure 15.25).


Figure 15.25 Sample introduction for NMR spectrometers. Left, automatic introduction of asample placed in an ‘NMR tube’ within the magnetic field produced by a superconducting coilmaintained at liquid helium temperature (reproduced courtesy of Varian). Right, a large magnetemployed for the introduction of a particular kind of sample – the human body (part of a MRIinstrument from SMIS).

15.16 HPLC-NMR coupling

The hyphenation of liquid chromatography with NMR spectroscopy is one ofthe most powerful and time-saving methods for the separation and structuralelucidation of unknown compounds and mixtures (Figure 15.26). Unfortunately,HPLC-NMR spectroscopy is a relatively insensitive method requiring sufficientsample concentration in the NMR flow cell. Bearing in mind the tendency towardthe miniaturization of HPLC and the consequent reduction of the quantities beingchromatographed, on-line coupling of HPLC with NMR offered a real challenge.The use of deuterated organic solvents for mobile phase is generally expensive.The principle consists of passing the mobile phase from the exit of the detector ofthe chromatograph to a microcell placed in the NMR apparatus. The quantity ofa compound in the probe depends about the detection volume.

There exist in principle two general methods for carrying out HPLC-NMR:on-flow and stopped-flow experiments.

With the on-flow mode of operation the output of the chromatographic sepa-ration is recorded simultaneous with 1H NMR spectra. In most cases the flowof the mobile phase is decreased to allow a large number of NMR spectra to berecorded of one chromatographic peak.

However if the quantity of compound is very small then it may be necessaryto interupt the flow of the mobile phase as soon as the maximum of the peakreaches the flow cell (indicated by UV detector). This stopped-flow mode is usedin order to accumulate hundreds of scans to improve the signal/noise ratio of theresultant spectrum.

15.17 FLUORINE AND PHOSPHORUS NMR 355

NMR

HPLC

Transfert lineHPLC/NMR

C

O

NH

CH

CH2

OH

CO2H

CH2

CH

C

O

NH

HC

CO2H

CH3

NH21

6

3 4 523 4 521

7

Gly-Tyr (t = 6.8 min) Phe-Ala (t = 9.4 min)

a

a

a

b

b

b

1H NMR

δ

Tim

e (m

in)

2 134567(ppm)

H2NCH2

δ 2 134567(ppm)

5,6 4

4

2,1,3 7

5 32 1

11

10

9

8

7

6

Figure 15.26 An experimental result by HPLC-NMR coupling. Separation of two dipeptides�5�g each) with identification of the signals. For more clarity the peaks of the solvents around2 and 5 ppm (acetonitrile and water) have been eliminated (Sweeder R.D. et al. Anal. Chem.1999, 71(23), 5335).

15.17 Fluorine and phosphorus NMR

Fluorine and phosphorus are the two heteroatoms in organic chemistry mostfrequently studied by NMR after hydrogen and carbon.

Fluorine element, consisting of 100 per cent 19F�I =1/2�, can be compared with1H for its sensitivity. Its electronegativity being greater than hydrogen (4 ratherthan 2.1), chemical shifts are distributed on a much greater range (Figure 15.27). Asa consequence, in 19F NMR, it becomes possible to distinguish between compoundsthat are chemically very similar. In particular, differences due to stereochemistryare significant with the coupling constants JF-H extended over a greater rangecompared to JH-H (Figure 15.17). On the other hand, relatively few moleculescontain atoms of fluorine. Therefore, the fluorine NMR spectra are generallyobtained from compounds to which a 19F (or a group CF3) has been intentionallyintroduced in a known position by chemical modification, in order to answerquestions of structure from the comparison of spectra. The fluorine atom inducesa chemical shift comparable to that of an hydroxyl (OH) group, but with minormodification in the stereochemistry of the molecule. The Van der Waals radius offluorine is 1.35 Angstrom instead of 1.1 for the hydrogen atom.

Phosphorus �31P I = 1/2� another common monoisotopic element, has beenstudied since the beginnings of NMR. It has a great sensitivity and it is an importantelement in the composition of numerous biological compounds.


Scale given in ppm with respect to the reference compounds

227 140 36 0 –238 –300

PH3Me3PO(MeO)3PPBr3

+250

31P H3PO4(85%)

+200 162 0 –64 –163 –200 –272 –300

19F

WF6

CFCl3

PhCF3C6F6 F– MeF

Figure 15.27 Positions of some NMR signals due to fluorine and phosphorus.

15.18 Quantitative NMR

Although NMR is a method essentially reserved for structural analysis, due tothe quality of the information that it can yield, it can be used also to givethe composition of mixtures. This application is possible if the signals chosenfor locating each constituent have areas which can be measured independently.Although the sensitivity and the precision vary with the type of nucleus, thismethod presents interesting features such as the possibility to carry out analyseswithout complicated sample preparation and whithout destruction of the sample.There is no risk of polluting the instrument and in contrast to many other methods,such as chromatography, there is no need of a prior standardization step. Fromthe molar ratios to which spectrum examination yields access, it is possible todeduce mass concentrations.

� In organic synthesis, 1H NMR permits to calculate the yields of a reaction. Finally,industry uses ‘low resolution’ analysers based upon 1H NMR to quantitate water andfats in food industry, like in many other fields.

15.18.1 Measuring areas – application to simple analysis

Areas of peaks on spectra can be given in the form of numerical values, or for olderapparatus, can be taken from the integration plots that are superimposed upon thespectrum (Figure 15.1). Yet it is difficult to measure signals to better than 2 per centaccuracy for various technical and physical reasons. NMR-lines are theoreticallyLorentzian curves, which are quite broad at their bases, and bear substantial areaseven under 1–2 per cent of peak intensity (usually in the noise region). In 13C NMR,it is preferable to add a relaxation agent in order to avoid saturation, linked to therelaxation times, which alters the intensities of the signals. The delay between succes-sive scans must be long enough to allow the magnetization to achieve equilibriumalong the z-axis (approximately 5 × T1 for the proton with the longest T1).

15.18 QUANTITATIVE NMR 357

Consider, for example, a sample comprising a mixture of acetone A and ofbenzene B diluted in CDCl3 as solvent. On the 1H spectrum of this mixture twosignals are observed at � = 2�1ppm (acetone) and at � = 7�3ppm (benzene), withrespect to TMS. This spectrum corresponds to the weighted superimposition ofthe two individual spectra (Figure 15.28).

In this particular case where the molecules of the two compounds each havesix protons, the ratio of the areas of the two peaks is representative of the rationA/nB of the respective numbers of molecules of A and B (given that the responsefactors are equal for A and B). Assuming that the mixture only contains these twocomponents, and designating SA as the area of the acetone signal and SB that ofbenzene, it follows that:

nA

nB

= SA

SB

(15.11)

If CA and CB are the concentrations expressed in percentage mass of A and B,of which the molar masses are MA and MB respectively, then:

CA + CB = 100

CA

CB

= nA · MA

nB · MB

(15.12)

Or, by substituing into expression 15.11:

CA

CB

= SA · MA

SB · MB

(15.13)

Therefore,

CA = 100 · SAMA

SAMA + SBMB

and CB = 100 · SBMB

SAMA + SBMB

(15.14)

15.18.2 Samples containing identifiable compounds

A more general case is that in which the signal (or signals) selected for eachcompound to be measured do not correspond globally to the same number of

3 28 7 6 5 4 1 0 ppm

δ

B A TMSSASB

Figure 15.28 1H spectrum of a mixture of acetone (A) and benzene (B). If SA =111 and SB =153(arbitrary units), then knowing that MA =58 and MB =78g/molCA =35% and CB =65% totalmass.


protons, either because the molecules do not have the same total number ofprotons, or alternatively, if only a portion of the spectrum of each compound hasbeen chosen in order to identify it.

Supposing for example, that the signal selected for compound A correspondsto a protons and the signal chosen for compound B corresponds to b protons(A and B do not represent acetone and benzene as in above section). When thespectrum of the mixture of A and B is recorded each molecule of B leads to asignal whose intensity is different to that of a molecule of A. The expressionsin 15.15 will remain valid provided corrections are inserted to take into accountthese differences. Each area must be divided by the number of protons that areat the origin of the selected peak, in order to normalize the relative area to oneproton of either A or B. Then substituing SA and SB by the corrected areas SA/aand SB/b, the two preceding expressions become:

CA = 100 ·SA

aMA

SA

aMA + SB

bMB

and CB = 100 ·SB

bMB

SA

aMA + SB

bMB

(15.15)

Expression 15.16 can be transposed to the case where n constituents are visibleon the spectrum. By using labels such as A, B, …, Z and in locating each consti-tuant by a specific area, ca. Si for i protons for the component I, the generalequation 15.16 giving the mass per cent of each one can be formulated :

Ci = 100 · �Si/i� · Mi

�SA/a� · MA + �SB/b� · MB + � � � + �Si/i� · Mi + � � � + �SZ/z� · MZ

(15.16)

With this type of calculation, 1H NMR is frequently used in organic chemistryas a method to find the yield of a reaction A → B. This is done by recordingthe spectrum of the coarse material after reaction and by identifying a signalbelonging to the product formed (B) and a signal belonging to the remainingstarting material (A). The yield of B with respect to A can be written using theprevious notations :

R = 100 ·(

SB

b

)/

(SA

a+ SB

b

)(15.17)

15.18.3 The internal standard method

A more general situation corresponds to the measure of a single compound in asample. To do that, it is not indispensable to know the nature of all the othercomponents that are present, or to identify all of the signals in the NMR spectrum.In fact, it is sufficient to find a signal belonging to the compound of interest.

In order to quantify compound X �M = MX� in a mixture called E, a quantitypR mg of reference compound R (with mass MR) for use as internal standard, is

15.18 QUANTITATIVE NMR 359

added to pE mg of the sample E containing compound X, before recording thespectrum. The standard R is chosen such that the signal serving as indicator doesnot interfere with the signal chosen to quantify compound X (Figure 15.29). Next,on the NMR spectrum of the mixture containing the internal reference, a signalbelonging to compound X (area SX for x protons) is chosen as well as a signalbelonging to standard R (area SR for r protons).

By designating nX/nR the molar ratio of X and of R, as before, expression 15.19can be obtained:

CX

CR

= nX · MX

nR · MR

(15.18)

knowing that

nX

nR

= SX/x

SR/r(15.19)

The concentration CR, expressed as a percentage mass of R, being equal to:

CR = 100 · pR

pE + pR

(15.20)

the mass concentration (per cent) CX of compound X can be deduced :

CX = 100 · pR

pE + pR

· �SX/x� · MX

�SR/r� · MR

(15.21)

15.18.4 The standard addition method

The previous method can be improved by preparing a number of standard solu-tions that contain both the sample and increasing quantities of the same compoundto be measured. From the corresponding NMR spectra of these solutions, a plotcan be drawn representing the area of the signal selected for the measurement as afunction of the quantity added. The intercept of the graph with the concentrationaxis will give the unknown concentration (Figure 15.30).

The difficulty of this method is in maintaining the stability of the NMR appa-ratus long enough to be able to undertake successive measurements of the standardsolutions.

X

TMSSR SX

Ref.

38 24 1 0 δ (ppm)7 6 5

Figure 15.29 Scheme displaying a spectrum of a sample into which a reference compound R hasbeen added. The signal X belongs to the compound to be measured and the signal S to theinternal standard.


Concentration by adding Xto the sample solution

0 2 4 6 8CX

SX

mL

Figure 15.30 Graph obtained for the standard addition method. The unknown concentrationcorresponds to the abcissa segment between the origin of the axis and the intersection with thecalibration curve.

15.19 Analysers using pulsed NMR

Pulsed wave Fourier transform NMR permits another form of routine measure-ment though rather yet underestimated by quality control analysists. Water andcertain other organic compounds such as fats can be quantified by this tech-nique from the hydrogen concentration in the sample. The corresponding instru-ments do not plot the usual NMR spectrum but give the global intensity of theFID immediately following the period of irradiation, as well as its time decay(Figures 15.31, 15.32 and 15.33). The rate with which the protons relax yields infor-mation about the environment of the hydrogen atoms. It thus becomes possibleto distinguish the protons that are present in a solid compound and those thatare part of a liquid. In food area, following standardization, this give access to theconcentration of water and fats in a variety of samples.

Rapid decay, typical of a solid sample

Slow decay, typical of a liquid sample

0 2 4 6 δ (ppm)

Inte

nsity

Figure 15.31 FID for a solid/liquid mixture. The amplitude of the FID which relates thequantity of protons as a percentage of the total mass, can be distinguished from relative measuresbased on T2„ which permits the percentage of solid to be determined in the sample throughdeconvolution of the curve envelope and its constituents, as displayed on the graph.

15.19 ANALYSERS USING PULSED NMR 361

Other applications follow the same principle and are based upon the detectionof phosphorus or fluorine elements.

� To determine the water resources of the subsoil (free water quantification anddepth discrimination of water-tables), geologists can base their investigations upon 1HNMR signals submittted to the low ambient Earth’s field by using a suitably adaptedequipment (the Larmor frequency is a few hundreds Hz).

Figure 15.32 Low resolution 1H NMR instrument for routine analyses. The analyser operateson the principle of pulsed NMR and is used for quantifying water and fat in numerous foodproducts (model minispec, reproduced courtesy of Bruker).

Figure 15.33 NMR research instrument. The typical appearance of these instruments corre-sponds, as here, to the combination of a superconducting magnet (at the bottom), of anelectronic cabinet and a workstation for the analysis of results. Model Avance 400 (reproducedcourtesy of Bruker).

Tabl

e15

.5N

MR

chem

ical

shif

tsof

prin

cipa

lty

pes

ofpr

oton

sin

orga

nic

mol

ecule

s(r

epro

duce

dby

perm

issi

onof

Spec

trom

etry

Spin

&T

echniq

ues

)

15.19 ANALYSERS USING PULSED NMR 363

Table 15.6 13C NMR chemical shifts of principal types of carbons in organic molecules

100 60 0204080120140160180200220

Ketones

Aldehydes

Acids

Esters

Alkenes

Aromatics

Hetero-aromatics

Hetero-atomics

Tert. C

Second. C

Prim.C

C = N

C = C

C = C

C = C

C = O

C = O

C = O

C = O

C C

C N

C – O

C – N

C – C

C – X

CH – O

CH2 – O

CH – X

CH – X

CH – C

CH3 – X

CH3 – O

CH2 – C

CH3 – C

CH – N

CH2 – N

CH3 – N

Scale in ppmrelative to TMS

Nitriles

Alkynes

Quatern. C


Problems

15.1 Often in tables the values describing a nucleus’ magnetic moment arerepresented as lying upon an axis parallel to �B, the applied magnetic field.Therefore, if for a proton, �z = 1�41 × 10−26 J · T−1, calculate the constant� for the proton.

15.2 If T = 300K, calculate the ratio of the populations NE1/NE2 for a protonin an NMR spectrometer where the applied magnetic field B = 1�4T.Make the same calculation for the case where the field B = 7 T, given that� = 2�6752 × 108 rad T−1 s−1.

15.3 In the 1H NMR spectrum from a 200 MHz spectrometer the scale alongthe abscissa is represented by 1ppm = cm.

1. What is the distance between two signals with a separationof 7 Hz?

2. If it is known that � H/� C=3�98, what would happen to the distancecalculated above if a 13 C spectrum were to be recorded on the sameapparatus?

15.4 1. Calculate the chemical shift, �, in ppm of a proton (1H), whose NMRsignal is displaced by 220 Hz with respect to TMS (the field of thespectrometer is 1.879 T).

2. The resonance signal for a proton is displaced by 90 Hz with respect toTMS when measured on a 60 MHz spectrometer. What would happento this displacement if an apparatus of 200 MHz was employed?

3. What would be the corresponding chemical shift of the same protonwith both of these spectrometers?

15.5 Two isomers A and B share the same molecular formula, C2 HCl3 F2. Whatis the structure of each of these isomers when their proton NMR spectra,as recorded upon a 60 MHz apparatus, are the following:

PROBLEMS 365

The spectrum of isomer A comprises two doublets at 5.8 ppm and6.6 ppm respectively �J = 7 Hz�, while that of isomer B contains a tripletat 5.9 ppm �J = 7 Hz�.

Consider now that a third isomer is present. Under the existing condi-tions, describe what its spectrum must be.

15.6 Numerous NMR experiments make use of the ‘Magic Angle’ techniquewhich corresponds to the angle made by the spin vector and an axis parallelto the direction of the magnetic field in which it is held. What is the valueof this angle in degrees?

15.7 25 mg of vanillin �C8 H8 O3� is added to 100 mg of an unknownorganic compound. The 1H integration curve displayed upon the spec-trum of the new mixture can be described as follows: one protonof the original compound corresponds to a value of 20 mm while asingle proton of vanillin corresponds to 10 mm. What is the molec-ular weight of the unknown compound? Remember: H = 1, C = 12,O = 16g/mole.

15.8 If the ratio of the magnetogyric constants �F/�H is 0.4913, calculate thedistance which would separate the TMS signal from that originating froman atom of fluorine, given that the scale upon the spectrum is representedby 1ppm = 2 cm. (The apparatus is a 200 MHz spectrometer.)

15.9 Following the reduction of acetone in isopropanol by means of ahydride the 1H NMR spectrum of the crude, isolated product reveals thatthe reaction has not completed. The integration curve of the remainingacetone corresponds to a value of 24 (arbitrary units), while that ofisopropanol is equivalent to 8. Calculate the molar yield of this transfor-mation.

15.10 From the 1H NMR spectrum below, which corresponds to a mixture ofbromobenzene, dichloromethane and iodoethane, calculate the percentagecomposition of the three components. The values (without units) givenin brackets on the integration curve are proportional to the areas of thecorresponding signals.


Given: H = 1, C = 12, O = 16, Cl = 35�5, Br = 80 and I = 127 g/mol.

PART 3

Other methods

Comet and Interstellar Dust Analyser (CIDA) is a time-of-flight mass spectrometer aboardNASA’s Stardust spacecraft launched in February 1999 to explore comet Wild 2 (mission 1999-2006). CIDA has been fabricated by Hoerner & Sulger, under contract by the German SpaceAgency.

368 OTHER METHODS

Trace analysis

Modern chemical analysis uses instruments of increasing sensitivity. This is not without logicsince more than half of the analyses performed today concern analytes of very low concentration,described as traces or ultra-traces.

The notion of trace is related to the corresponding mass concentration in the sample. Byconvention, a compound is considered as being present in trace amount when its concentrationin the environment is less than 1000 ppm. Beneath 1 ppm (1 �L/L or 1 mg/kg), an analyte isconsidered as being at the ultra-trace level.

Obviously, these limits are not always so clear. They depend upon the analyte, the matrixand of the use of the matter analysed. Even these terms have a subjective character. Thus, if asample of acetone, in use as a solvent, contains 0.1 per cent methanol, then it can be said thatthe latter is a trace (1000 ppm) but if the sample constitutes drinking water, then it would beconsidered an enormous quantity.

To carry out these analyses, the detection limit of the instrument must be imperativelyknown. This is defined as the concentration of an analyte that allows to obtain a detectablesignal with certainty – for example, three times the standard deviation of the background noisesignal or of the blank. The detection limit is expressed in parts per million (defined by themass/mass or mass/volume ratio, depending upon the matrix). If the mass or the volume ofsolution needed by the instrument to obtain this result is well defined, the preceding value canbe transformed to the absolute quantities of analyte or mole fractions (picomole, femtomole,etc.) for obtaining this signal. In general these values are excessively small because currentinstruments only require minute volumes of sample.

By way of example, if 1�L of a 1 ppb solution (being about 1 pg), is injected into achromatograph, and if a mole of the analyte weighs 100 g, this will be 10 femtomol! From thispoint the analyst must become familiarized with prefixes such as femto- �10−15�, atto- �10−18�,zepto- �10−21�. A zeptomole contains only 602 molecules of a given compound. These quantitiestend towards single atoms or individual molecules. The ultimate trace is almost attained.

The detection of individual species is possible with certain methods. Fluorescence methodsare used for the detection of molecules and Accelerator mass spectrometry (AMS) for detection oflong-lived nuclides. The conventional method of counting the 14C beta-decays is now abandoned,still it is a method that can record the signal of a single atom. This paradox is explainedby taking into account that to locate a radioactive atom by counting, it is necessary thatdecomposition occurs during the time of the measurement. If the lifetime of the radionuclide islong, the chance of observing this event will be small.

AMS can measure the ratio of a rare radioisotope relative to a more abundant stable isotopeof the same element as for examples 14C/13C or 3H/1H. This provides a new way to measureattomoles of radiocarbon and some other radionuclides.

If the majority of the methods used for trace analyses are the same as those normallyemployed to measure more abundant compounds, much more care is needed. Many difficultiesappear. At this level, containers, flasks and reagents become polluted and the work must becarried out in a clean room, otherwise in the absence of much precautions, it will be possibleto discover literally anything, anywhere – it will be just to choose the species to hit upon.

16Mass spectrometry

Mass spectrometry (MS) is an analytical method of characterizing matter, basedon the determination of atomic or molecular masses of individual species presentin a sample. The instruments employed for carrying out mass spectrometry canbe classified into different categories according to the mass separation techniqueused. Some are derived from assemblies developed at the beginning of the 20thcentury for the study of particles or ionized atoms submitted to a magneticfield, while others rely upon different principles. Continuous improvements havemade mass spectrometry the most versatile, sensitive and widely used analyticalmethod available today. Miniaturization and the emergence of new ionizationtechniques allow to this method to be present in a variety of sectors: organicand inorganic chemistry, biochemistry, clinical and environmental chemistry, andgeochemistry. This technique is found in many industrial control processes as wellas for regulation compliance.

16.1 Basic principles

A minute quantity of sample, transformed in the gas phase or in a suitable form,is ionized and the resulting charged species are then submitted, in an enclosedspace maintained under high vacuum, to the action of an electric and/or magneticfield, depending on the type of instrument. The study of the forces exerted uponthe ions allows the determination of their mass-to-charge ratio and, eventuallytheir nature. This method destroys the compound sample, but owing to the greatsensitivity of the technique, only a tiny quantity is required.

� By way of example, the ions resulting from a sample of methanol (CH3OH)transformed to the gaseous state and then ionized by bombardment with electrons,will include amongst the charge-carrying species a small amount of positive ionsCH3OH+. These ions, formed in an excited state, possess a surplus of internal energythat will induce for many of them an almost immediate fragmentation. They do not,however, all dissociate by the same pathways, thus leading to different ion frag-ments whose mass is less than that of the original methanol molecule. Generally


370 CHAPTER 16 – MASS SPECTROMETRY

m/z29

0

50

100(a)

(b)

(c)

m/z 12(3), 13(5), 14(10), 15(41), 16(2),28(12), 29(72), 30(9), 31(100), 32(67), 33(1)

5 10 15 20 25 30 35 40

72 180.05 180.10 180.15

CH3OH

m/z

[M - CO]+

180.0933

[M - C2H4]+

180.0580

6741

1210

93

100

321

32

25

Figure 16.1 Fragmentation spectrum and mass spectrum presented in graphical or tabular form.(a) Fragmentation spectrum of methanol; (b) Unconventional representation of the same spec-trum in the form of a circular diagram (hollow pie chart): statistically, for 321 ions formed,there are 100 of mass 31 u (Da), 72 of mass 29, etc. The various ions constitute many differentpopulations; (c) Section of a high-resolution recording of a compound M presenting two ionswith very close m/z ratios (one due to loss of CO and the other due to loss of C2H4).

these fragments, formed by simple bond cleavage and from subsequent rearrange-ment reactions are carriers of information on the structure of the original molecule(Figure 16.1a).

The results are displayed as a graph called mass spectrum and presented inthe form of the abundances of the ions formed and classed in increasing orderof their mass/charge ratio (Figure 16.1). Operating under identical conditions,the fragmentation is reproducible and therefore is a means of characterizing thestudied compound.

Since mass spectrometers create and manipulate gas-phase ions, they operatein a high-vacuum system. They consist of three essential parts: an ionizationsource, a mass-selective analyzer, and an ion detector. The sample is submitted toa succession of steps:

1. Ionization: the sample in the form of gas or vapour is ionized in the sourceof the instrument. At this stage the mass spectrometer generates gas-phaseions by one of the numerous procedures existing. All molecules lead to astatistical distribution of fragment ions.

16.1 BASIC PRINCIPLES 371

2. Acceleration: once formed the ions are immediately extracted from this partof the instrument to be focussed and accelerated by a series of electroniclenses, to increase their kinetic energy.

3. Separation: the ions are then ‘filtered’ by the analyser according to their mass-to-charge ratio, a number of instruments combining several mass analysersin series.

4. Detection: after separation, ions terminate their flight by striking the sensorof the detector which measures electrical charge and amplifies the weak ioniccurrent.

5. Display of the mass spectrum arising from treatment of the signal sent by thedetector.

� This method only yields the mass-to-charge ratio of the ions, m/q. Logically tocalculate m, q must be known. Since these ions carry a net charge of type q = ze(where e represents the elementary charge of the electron and z is a small integer),m can be determined to the closest factor of z. This is why the scale of the spectrumis indicated as m/z (m being in atomic mass units). For molecules of small or mediumsize (M < 1000), which generate ions, generally all of them carrying a single charge(z = 1), the increasing order by mass is therefore the same as that of the ratio m/z.This assumes that the spectra are graduated in unified atomic mass units (u) ordaltons (Da). m/z is normally expressed in Thomsons (Th) but this unit has neverbeen widely accepted.

Ion abundance can be recorded in two very different ways:

• The normal-mass spectrum of the mass interval selected. The graph corre-sponds to a collection of signals in the form of peaks of different width,depending upon the resolution of the instrument (Figure 16.1c). These peakslead to the determination of the ion masses and can attain a precision betterthan 10 parts in a million �10−5 Da�. The upper mass limit, which is constantlybeing improved, can exceed 106 Da.

• The fragmentation spectrum (bar spectrum or stick plot). This correspondsto the distribution of all the ions formed, grouped by their nominal mass(cf. Table 16.1) as close to their exact masses and presented in the formof vertical lines. The most abundant type of ion leads to the most intensepeak, called the base peak, which is given 100 per cent intensity. The inten-sities of the other peaks are then expressed as percentages of the base peak.This graphical representation of masses distributed by population, whoseheights are proportional to their abundances, is essentially a histogram(Figure 16.1a, b). Bar spectra such as these are easy to archive and can be usedto further comparison and identification. This normalized display, which is


incidentally the most commonly used graph in MS, has however the incon-venience that two or more ions of different atomic composition can occur atthe same nominal mass.

The expression ‘mass spectrum’ must not lead to a confusion: the appa-ratus does not lead to a spectrum in the most usual sense of the term,that met in methods based upon the interaction between a sample andlight radiation. The origin of this expression arises most probably from thesimilarity between the recordings obtained from the first instruments usingphotographic plates with those of optical spectrographs giving a spatiallypresentation of resolved spectra. Mass spectrometry does not belong to opticalspectroscopy.

Mass spectrometry has progressively become an irreplaceable means of inves-tigation of compound structures in organic chemistry and biochemistry (notablyin proteomics). The technique can be applied to analysis of the elemental compo-sition of inorganic samples (ICP/MS) whilst also allowing to study mixtures ofmolecular species, when combined with chromatography. The on-line couplings,such as GC/MS or HPLC/MS are amongst the best methods of analysis for mixturesand samples containing trace amounts of analyte.

The identification of molecular compounds by mass spectrometry can beachieved from either of the two types of spectral diagram:

• Attempting to reconstitute the structure of the compound in the manner ofa puzzle. This is an exercise, which becomes more difficult as the mass of theoriginal molecule increases. Successive fragmentations of the ions make iden-tification more complex. However this task becomes less arduous if severalspectra recorded under different conditions are available with appropriatesoftware to help in their interpretation.

• Using a spectral library comprising a large number of fragmentation spectraamongst which, in a favourable case, might be found the mass spectrum ofthe molecule in question.

16.2 The magnetic-sector design

Early mass spectrometry started with the first experiments by J.J. Thomson (1900)and the use of a magnetic field to determine the m/z ratio to study isotopes wasdeveloped by Aston or Bainbridge in ca. 1930 (Figure 16.2). The classical equationsthat describe the movement of ions in magnetic or electric fields are the same onwhich are based a number of currently mass spectrometers.

In this assembly, the positive ions generated are first accelerated through avoltage difference U . They take up a velocity v which depends upon their massm (cf. Section 16.3.1) and are then submitted to a transverse magnetic field �B

16.2 THE MAGNETIC-SECTOR DESIGN 373

+

+

+Velocityfilter

mvF

B

to vacuum

Source

B

Photographicplate

Ne22

Ne21

Ne20

Ne

Ions

e–e–

20 21 22 20 21 22

Ne++ Ne+ •

B

FBFE +

Ne++Ne+ •

–

–

–

–

+

+

e––

Figure 16.2 A 180 � magnetic deflection spectrograph with a velocity filter. The filter eliminatesthe problem due to the quasi impossibility of having homogeneous and mono-kinetic beams.The diagram represents a sort of photographic recording of the spectrum of neon. The twoseries of broken lines represent the removal of one or two of the electrons from the differentisotopes of elemental neon. The symbol +· signifies that the ion is both a radical (i.e. hasan unpaired number of electrons) and a cation. J.J. Thomson, who around 1913 proved theexistence of the isotopes of neon, is considered as the father of this kind of assembly. Later,work performed by F.W. Aston showed the existence of the isotopes of sulphur and chlorine.

responsible for a magnetic flux of density (or field intensity) B. The orientationof field does not modify the ions’ velocity but rather forces them on a circulartrajectory of which the radius is a function of their m/z ratio.

The fundamental relationship of dynamics, �F = m · �a (�a designates the acce-leration), applied to ions of mass m on which is exerted the Lorentz force �F =q · �v ∧ �B leads, after arrangement, to the following relationship:

�a = q

m�v ∧ �B (16.1)

The orientation of �H is such that only the centripetal component of the accelera-tion vector �a gets involved. The ion trajectory lies in a plane perpendicular to �Band containing �v. Since a = v2/R, by substituting a by its form in equation 16.1(where q = ze is in coulomb, v is in m/s, B is in tesla and m in kg), expression16.2 is attained which shows that separation occurs according to the moment ofthe ions:

R = mv

zeB(16.2)


Therefore, the m/z ratio of the ions is only obtained if their speed is known(Equation 16.3):

m

z= RBe

v(16.3)

For this, in older instruments, a device situated prior to the magnetic sector,called a velocity filter was employed. This was done by submitting the ions totwo opposing forces through the action of both an electric �E and a magneticfield �B. Only the ions remaining on the central trajectory were able to exit thefilter. Because the net resulting force must be zero, then qE = qvB and thereforev = E/B.

� Coulombic force (EMF) and Lorentz force law: When a potential difference of �Vvolts is applied between two parallel plates separated by a distance d, an electricfield �E (V/m) appears, which is uniform and oriented towards the lower potential, ifthe environment is homogeneous: thus �E =�V / d. The field �E determines the Coulombelectrical force �F acting upon an ion carrying a charge q, whatever its mass andposition in the field. F = qE (if the ion is carrying a single elementary charge, q = e= 1.6 × 10−19 C). The coulombic force exerted is independent of the velocity of theion.

The force that is exerted on a charged particle carrying a charge q, possessingan instantaneous velocity �v and submitted to the action of a magnetic induction B, isgiven by the Lorentz force equation:

�F = q�v ∧ �B� (16.4)

In the general case, when there is an electric field, a positively charged ion will beaccelerated in the orientation of �E, but will spiral when moving through �B, due to theorientation of the cross-product operator. When there is no electric field, it holds inany reference frame. This equation 16.4 is deduced from Laplace’s force law whichstates the force experienced by a conductor of length dl, through which passes acurrent I, in a magnetic field �B. The orientation of this force (d �F = I · d�l ∧ �B) can befound from different approaches such as the right-hand three-finger rule or using theorientation of a direct trihedron.

16.3 ‘EB’ or ‘BE’ geometry mass analysers

Present-day spectrometers with in-built magnetic sectors are the result of thetechnological evolution of previously double focusing magnetic mass analysersused by Mattauch and Herzog or Bainbridge by the end of the 1930s. They leadto very accurate m/z ratios, though they are limited in the study of high molecularmasses (this is the difficulty of producing magnetic sectors of large volume). Theseinstruments also include an electrostatic sector that can be located between the ionaccelerator and the magnetic sector (forward geometry, ‘EB’) or after the magnetic

16.3 ‘EB’ OR ‘BE’ GEOMETRY MASS ANALYSERS 375

Sample Ionisationchamber

Ionaccelerator

DetectorElectrostatic

sector EMagnetic analyserB

Figure 16.3 A double focusing magnetic sector instrument showing its ‘BE’ geometry. Model JMS700. On this photograph, the characteristic shapes of the electromagnet (magnetic sector) andof the electrostatic sector can be seen. The detector lies at the right the ion source is on the left(reproduced courtesy of Jeol, Japan).

sector, as on Figure 16.3 (reversed geometry, ‘BE’). The function of the electricsector is to focus the energy of ions produced in the source. Energy focusing leadsto a significant improvement in resolution, as we will see later.

� With a technique known as electromagnetic separation, applications of mass spec-trometry began to spread away from the previous academic work into more practicalfields like nuclear isotope enrichment. Mass spectrometers have been engaged ona preparative scale (calutrons), notably in the United States where in 1943 severalkg of 235U destined for the manufacture of the first atomic bombs were isolated (theManhattan Project). This, now dated, procedure, which has a low flow rate of under10-3 Pa, is still occasionally in use by other countries.

16.3.1 Ion accelerator

Approximately 5 per cent of the positive ions formed either before or in theionization chamber or elsewhere in the spectrometer, depending upon the type ofinstrument, will finally reach the detector. The ions must first be accelerated bymeans of a series of plates of increasingly negative potential, the total acceleratingpotential U can be as high as 2 to 10 kV (Figure 16.4). The process must beconducted under a good vacuum �P < 10−4 Pa� in order to avoid the formationof electric arcs and to minimize collisions between ions. Under these conditions


Ene

rgy

ΔE1

ΔE0

Δv1Δv0Velocity

Figure 16.4 Influence of the accelerating voltage upon the range of velocities for ions with thesame mass. Assuming the range of velocities prior to acceleration is represented by �v0, it canbe observed that the range of velocities after acceleration, �v1, is much smaller. ��E1 =�E0 but�v1 << �v0�.

all the ions carrying the charge q = ze, acquire the same kinetic energy E1 = zeU(relation 16.5). Their velocity after acceleration is therefore inversely proportionalto the square root of their mass mi (Equation 16.6).

E1 = zeU = 1

2miv

2i (16.5)

vi =√

2zeU

mi

(16.6)

However, since the velocities of ions before acceleration are non-zero, their totalkinetic energy must take account of their initial kinetic energy, E0, which is smalland unknown:

E�total� = E1 + E0 (16.7)

The mass accuracy will depend of the velocity of the individual ions with the samemass. For this reason, a high accelerating potential U will restrain the range ofvelocities for ions of the same mass (Figure 16.4).

16.3.2 Electric sector

An electric sector made of two concentric and cylindrical electrodes is used tofurther improve the precision of the mass measurements (Figure 16.5).

The force exerted upon the ions, forced to travel tangentially in the electricsector, does not modify their kinetic energy, as the force is perpendicular to theimposed central trajectory that has a radius of curvature R′ (Figure 16.5). Its

16.3 ‘EB’ OR ‘BE’ GEOMETRY MASS ANALYSERS 377

Electrostatic sector

Magnetic prism

Collectingplate

Source

Mattauch-Herzog assembly (dispersive apparatus E-B)

Magneticsector

Magneticprism

Treatmentof the signal

Ionisationchamber

Sample

Electrostatic sector

Electrostaticsector

Vacuum

O

Ion collector

R

Vacuum

R′E

F2+

U

+

– –

Nier-Johnson assembly (E-B)

Detector Source Detector

Source

magnetic prism of homogeneous field

m/z

1, Light ion2, Heavy ion

F1 F2

+(a)

ions (+)

1953

F1 F2

(b)

O

(c)

E

E

B

B

1

1935

(d)

2

Figure 16.5 Mass spectrometer with magnetic analyser. (a) Nier–Johnson assembly; (b)View of the directional focusing by the magnetic sector (the entrance and exit planesare oblique with respect to the angle of incidence of the beam, ensuring focusing); (c)Mattauch–Herzog assembly; (d) Arrangement of a double focusing spectrometer (e.g. R′ = 40 cmand R = 60 cm).


intensity is equal to F = mv2/R′. Replacement of the term mv2 by its equiv-alent in terms of acceleration voltage �mv2 = 2zeU�, leads to expression 16.8,which fixes the transmission conditions of the ions through this radial filter.When E and U satisfy this expression, only the ions having acquired the properenergy under acceleration due to the potential drop V , will follow the trajectoryof the radius R′ and be able to leave the filter. This device acts as an energyfilter. Moreover, the electric sector has direction-focusing properties. It can bringinto focus ions, restoring the trajectories which are somewhat deviating beforeentering the sector. Knowing the potential drop V between the plates of thesector, d distance apart, E can be determined and also the correlation between Uand V :

E = 2U

R′ = V

d(16.8)

16.3.3 Magnetic analyser

In the EB configuration, a magnetic analyser (or sector) is located after the electricsector. The instruments of this type can be divided into two main categories:the Nier–Johnson geometry in which the radius of curvature imposed upon theions by the magnetic field is in the same direction as that in the electric field,and the Mattauch–Herzog geometry where these two curvatures are in oppositedirections (Figure 16.5). In the latter assemblage, if the magnetic analyser has aproper geometry, all masses are simultaneously focused in the beam, which isa necessary condition for spectrometers housing several detectors that measureisotope ratios. By eliminating the velocity v by combining the expressions 16.2and 16.5, the deflection (or focusing) equation (16.9) is attained for a magneticsector:

m

z= R2B2e

2U(16.9)

Only the ions which have followed the trajectory with radius R within the flighttube imposed by the instrument will be detected. Hence, to obtain a spectrumwithin a given mass range, the intensity of the field �B has to be progressivelymodified. All ions, whatever the m/z value, will successively follow, one after theother, the unique trajectory leading to the detector. Such a scan requires around0.1 second.

� The interdependence of m and U is the origin of a comparative method for a precisedetermination of masses, called peak matching. For this, along with compound X,the precursor of the ion whose mass is to be determined exactly, a mass standard isinjected (usually a perfluoro compound whose fragment ions masses are known withhigh precision). An ion whose mass is close to that of the mass to be determined ischosen as a reference (for example, if the unknown mass is in the order of 200 u,the C4F8 ion which has the mass 199.9872 u can be taken and for masses close

16.4 TIME OF FLIGHT ANALYSERS (TOF) 379

to 12, the peak of carbon 12 can be used, which is 12 u by definition). This task isperformed automatically on modern instruments.

Both the unknown and the reference peak are forced to overlap. At this pointexpression 16.10 is verified, and mX can be calculated:

mx/mref = Uref/Ux (16.10)

The magnetic sector is, like the electric sector, focusing in direction: a beamof ions of the same mass and kinetic energy reaching the magnetic sector by F1

with a small angular dispersion �, is re-focused in F2, image of F1. At any instantduring the scan only ions with a defined mass can follow the radius of curvature R(Figure 16.5). The combination of magnetic and electrostatic deflection of the ionsallows focusing on the basis of both momentum and kinetic energy, thus allowinghigh-resolution mass spectrometric analysis (directional and energy focusing). Inmagnetic sector instruments, the dimensions and the weight of the magnet limitthe mass range.

16.4 Time of flight analysers (TOF)

The principle underlying time of flight mass spectrometers is based on the rela-tionship that exists between mass and velocity of the ions at a given kinetic energy.The instrument which use a pulsed ionization, measures the time necessary for themasses to travel a distance L in a field free tube, under high vacuum (Figure 16.6).The basic relationship of linear TOF analysers is obtained by eliminating thevelocity v from expression 16.5, knowing that L = vt:

m

z=(

2eU

L2

)t2 (16.11)

In practice, TOF spectrometers enable the analysis of very high masses (300 kDa).To evaluate the masses with precision requires overcoming the initial energyand spatial distributions of the ions. Resolution is related to the duration ofthe ionization pulse. It can be increased using almost instantaneous ionizationmethods (a few nanoseconds with a pulsed laser), repeated several hundred timesper second, in order that the ions are ejected at the same time. Many instrumentscontain a reflectron to compensate for kinetic energy distribution of ions of thesame mass (Figure 16.6). With this kind of electrostatic mirror, the most rapidions (i.e. higher energies), will penetrate deeper into the decelerating zone thanlow energy ions, less strongly repelled. The same electrical fields that slowed theions down as they entered the reflector will now accelerate them back out of thereflector so that they leave with the same velocity that they entered it. In this waythe ions of the same mass are time focused, then will arrive on the microchanneldetector at the same time.


Flight tube (e.g. L = 1 m)

1 3 3′ 4 5

6

L

m3+m1+ m1+m2+m2+

Vacuum10–5 torr

Laser Effect of the reflector + ++

2

To the continuousdynode (or microchannel)detector (the ion in white is slightly faster than the black one)

Ions of different velocitiesin two pathways

Vacuum

Ion source

+++ ++m3+

+

–

Figure 16.6 A simplified schematic of a time of flight spectrometer and the principle of the ionreflector (reflectron). (1) sample and sample holder; (2) MALDI ionization device by pulsedlaser bombardment; (3 and �3′� ions are formed between a repeller plate and an extrac-tion grid (PD 5000V) then accelerated by an other grid; (4) control grid; (5) microchannelcollector plate; (6) signal output. Below, a reflectron, which is essentially an electrostatic mirrorthat is used to time-focus ions of the same mass but which have initially different energies.The widths of the peaks are of the order of 10−9 s and the resolution ranges between 15 to20 000.

� Ion mobility spectrometers (IMS). This category of portable and fieldable analyticalinstrument is adapted for research into known and targeted compounds that can bevaporized. Ion mobility is the technique applied most frequently in explosives scanners(airports, terrorist attacks, chemical weapons). They are based upon the time takenby the ions to flight a short drift channel (a few cm) at ambient pressure (Figure 16.7),from ionization chamber to the detector. This technique, which differs from the TOF, towhich regrettably it is sometimes compared, is closed to a gas-phase electrophoresis.In the environment of the ion source which contains a radioactive beta particle emitter(63Ni), the presence of air leads to ionic aggregates (clusters) [(N2)x (H2O)y H]+

and [(N2)x (H2O)y O2]- that will react with the molecules of the sample compoundpresent, depending on their electron affinity. This chemical ionization process formsan aerosol, which migrates in a few milliseconds under the effect of a strong anduniform electric field gradient of about 15 kV/m, which accelerates them towards thedetector. The velocity of the ions depends not only on the mass, the charge and thesize or shape of the ion, but also on the temperature and pressure of the air. Thethreshold of detection can reach a few ppb. On calling the speed v, L the distancetravelled during the time tM in the field E, (E = V/L) expression 16.12 is obtained:

Kion = v

E= L

t M· L

V(16.12)

16.5 QUADRUPOLE ANALYSERS 381

Ion collectorReactant ions (air)Reaction ions

Upstream grid Electrodes Aperture gridDrift gas(Air inlet)

Sample inlet

Air

outle

t

63NiSource

M

NO–

NO–

10 15 20 ms.

O2F

–

curr

ent,

Arb

. uni

ts

curr

ent,

Arb

. uni

ts10 15 20 ms.55 drift time drift time

Drift region

Electric field

–

Figure 16.7 Ion mobility spectrometer. The ions are admitted into the analyser tube by control-ling the polarity of the entry grid. Below, an example of a recording obtained from gaseouscompounds. Armies in many countries use this technique for the detection of chemical warfareagents.

The proportional constant (Kion) is called the ion mobility and is usually computedin units of cm2 V-1 s-1. Kion is defined by a relation borrowed from capillary elec-trophoresis.

16.5 Quadrupole analysers

Besides the preceding mass spectrometers, other instruments less voluminous, oflower performance and less expensive have been developed for use in applica-tions that do not require high-resolution spectra. In this category are situatedinstruments including electric fields only, based upon the use of quadrupolemass filters. These spectrometers, which form the largest category, are veryuseful as mass detectors (GC/MS or HPLC/MS or ICP/MS installations) as wellas in a variety of industrial applications for gas and residual gas in vacuumindustry.

16.5.1 Potential and electric fields in a quadrupole

A classic quadrupole is formed of four parallel metallic rods �L = 5–20 cm� ofhyperbolic cross-section in the interior of the assembly (Figure 16.8). These four


O

y

z

x

+U –U

y

x

–

+

–

–

+ +

Figure 16.8 Diagram of a quadrupole. Notice the pairing of oppositely charged electrodes.This mechanically simple device requires high-precision manufacture of the rods machined tothe hyperbolic shape. In many models the rods have the size of a ball-point pen. Right, graphof a series of equipotential hyperbolic lines in the central part of the filter.

rods are electrodes that are coupled in pairs. The separation between twodiametrically opposed rods is designated as 2r0. If a potential difference Uis applied across the pairs, the potential �E for all points within the xy-plane,irrespective of z, will be given by:

�E = U · x2 − y2

r20

(16.13)

�E remains between +U and −U . For a homogeneous medium, the electricpotential �E is therefore zero all along the z-axis.

Expression 16.13 implies that in all xy-planes the points having the samepotential are situated on the branches of an equilateral hyperbola of which theasymptotes are the straight lines y = ±x. The field lines are orthogonal to theequipotential curves for each point Mxyz of the space inside the quadrupole. Thisfield has the value:

�E = −grad�E

The voltage at the surface of each electrode inside the quadrupole is given by:

‘x electrode’ �E = +U ⇒ y2 = x2 − r20

‘y electrode’ �E = −U ⇒ y2 = x2 − r20

When a positive ion penetrates via the origin O into the filter maintained undervacuum, the components of its velocity vector in xyz-space, represented by �x� y� z�,will determine its trajectory. The central zone behaves like a tunnel along thez-axis, whose walls can attract or repel an ion depending upon the ion’s position.

16.5 QUADRUPOLE ANALYSERS 383

The two positively charged electrodes focus it along the z-axis, which corres-ponds to the bottom of a potential valley (stability zone), while the two negativelycharged bars, in contrast, have a defocusing effect (appearance of an mound ofpotential in the yz-plane).

� The image of a marble made to roll along the bottom of a horizontally orientedguttering pipe bears a close similarity to a potential valley. To imagine the effect of amound of potential, the marble should be imagined as trying to roll along a length ofpipe on the outside, a very unstable pathway.

16.5.2 Use of a linear quadrupole as an ion filter

An a.c. voltage of radiofrequency and of maximum amplitude VM is superim-posed to the DC potential U ( is in the order of 2 to 6 MHz and VM/U of6 MHz). The two sets of electrodes are submitted to this alternating voltage, butout of phase by (Figure 16.9).

VRF = VM cos�2t� (16.14)

z

x

y

O

z

x

y

O

O

y

z

x

– U + VRF

Mass

tran

smis

sion

Tra

nsm

issi

on

Tra

nsm

issi

on

Focusingplates

xOz plane; high pass filter yOz plane; low pass filter

Mass Mass

ion M1

Ions Rods

a resonant iona non-resonant ion

Exit todetector

t1 t2Scan...

+ U – VRF

ion M2

+

+

–

–

Figure 16.9 Quadrupolar filter. Depending upon their mass, the ions respond more or lessto the demands of the variable field. Their travel time must be superior to the period of theradiofrequency. For this reason they enter the filter with a weak kinetic energy of several tensof electron volts.


Over time, for each point inside the filter, the potential now corresponds to thealgebraic sum of the expressions 16.13 and 16.14:

�EXY = �U + VM cos�2t��x2 − y2

r20

(16.15)

The resulting field within the quadrupole is made up partially of a fixed voltageand partially of a variable voltage. Under these conditions the ions which penetrateat O into the quadrupole are submitted to a force that is variable in both intensityand direction. They will follow complex three-dimensional and generally unstabletrajectories in the form of a helix or corkscrew. These pathways will generallyterminate on contact with one of the electrodes.

To obtain the equations of the movement of an ion the forces FX, FY and FZ

exerted upon it must be known (Mathieu equations). As this operation involvescomplex computation, only two particular cases will be considered here.

1. Assume an ion has a zero velocity component along the y-axis: its trajec-tory will remain in the xz-plane. The walls being alternately positive andnegative �VRF >> U�, the heavy ions, due to their high inertia, will notsubstantially respond to the variations in field orientation: they will only feelthe continuous positive voltage U and so will not be perturbed very much.They remain focused on the central axis. However, the lighter ions will beable to oscillate more and more until they discharge, that is be lost, on oneof the rods. The two positive rods constitute what is known as a high-passfilter.

2. Consider now the case of an ion that does not have a velocity componenton the x-axis: its pathway will remain in the yz-plane. The heavy ions willcontinue to be inexorably attracted towards the negative bars. Only the lightions that can rapidly react to the influence of the radiofrequency will betransmitted. The yz-plane constitutes a low-pass or highcut filter.

The calculations related to this technique expose that there are two ways ofusing this quadrupolar filter: one method in which the two voltages, U and VRF, aremaintained constant while , the radiofrequency, is scanned, or a second methodin which the frequency is maintained at a given value and the amplitude of thevoltages U and VRF are increased regularly in such a way that their ratio remainsat a invariable value.

In this way a band-pass is defined, for example 1 u width, unit of resolution,which permits the mass spectrum of the compound to be obtained in a sequentialmanner.

The resolution R of a quadrupole filter (for details see section 16.8.3) is relatedto numerous parameters. The instrument can be used either in a mode where �mis constant – in which case the resolution increases with the mass (Figure 16.10) –or in a mode in which the resolution is constant, close to 1 u.

16.6 QUADRUPOLE ION TRAP ANALYSERS 385

m/z

29

4143

55 57 69

71

18 (H2O)

Figure 16.10 Partial spectrum of a hydrocarbon obtained with a gas analyser operating underthe quadrupole filter principle. The recording reveals that the instrument has been used in themode for which �m is constant for the whole range of masses.

The maximum resolution is given by expression 16.16 for an ion carrying aunit charge e, accelerated under a PD of Vz volts at the entrance to a filter oflength L and of radius r0 by using a radiofrequency whose maximum voltageis Vmax.

R = Cste · L2 · Vmax

r0 · e · Vz

(16.16)

16.6 Quadrupole ion trap analysers

Other mass spectrometers are equipped with three-dimensional ion traps of whichthe geometry is much different to the quadrupoles previously described. In anion-trap, the ions are confined between three electrodes (one toroidal and twoend-caps), whose particular shape appears to result from a sort of anamorphosisof the four-bar set-up of a classic quadrupole. As in the previous category theyoperate under the effect of a variable electric field (with or without a superim-posed fixed field). Although they are, in appearance, physically simple devices,the fundamental principle of ion trap is complex. These ion trap detectors aresensitive, less costly than quadrupoles and compatible with different ionizationtechniques. The volume defined by the electrodes, named superior, inferior andannular, is simultaneously the ion source and the mass filter (Figure 16.11).These analysers are almost exclusively linked with a separative technique(GC/MS).

The functioning principles can be discussed as follows: the compound issubmitted to a very brief electron bombardment yielding ions which subse-quently penetrate the central part of the filter. A radiofrequency voltage is thenapplied to the annular electrode that confines these ions to the central space,by forcing them to follow complex trajectories in the presence of a low pres-sure of helium, of about 0.01 Pa, introduced to the trap as a form of shockabsorber.

To analyse the ions present, the radiofrequency amplitude is increased grad-ually to destabilize the ions. One by one, in the rising order of m/z ratio,


(a)

O

z

r0

(b)

1

3

2

Source

+

+

+

+ + + +

Detector

+

Figure 16.11 Ion-trap spectrometer. (a) Design of the electrodes in an ion trap; (b) Diagramgiving a perspective of the end-cap and annular electrodes (from Current Sep. 1997,16 : 3, p 85).

the amplitude of oscillation of the ions grows in the axial direction untilthey are eventually ejected through a series of small holes pierced in one ofthe end-cap electrodes behind which stands an electron multiplier as detector(Figure 16.12). If a reagent gas is introduced concurrently into the trapto react with the sample then a chemical ionization can also be obtained(section 16.10.2).

These small volume and high sensitivity instruments have, however, the incon-venience of operating over a narrow dynamic range and with an average repro-ducibility of spectra from the same sample, which represents a serious disadvantagein quantitative analysis.

(a) (b)

z

ro

O

Figure 16.12 Modelling of the ion pathway in a trap. (a) Trajectories of a stabilized ion;(b) Pathway of an unstable ion terminating in contact with one of the electrodes (the layout ofthe trap is the same as in Figure 16.11).

16.7 ION CYCLOTRON RESONANCE ANALYSERS (ICRMS) 387

16.7 Ion cyclotron resonance analysers (ICRMS)

These mass spectrometers, not widely used, are rather rare compared to theprevious ones. Basically a magnetic ion-trap, a ICRMS is able to ascertain themass of ions with great precision. The mode of operation can be described in thefollowing way:

The ions, obtained through one of the numerous existing procedures, aredirected towards a small cavity situated in the centre of a very intense magneticfield �B (4 to 9 T) produced by a superconducting coil. In this chamber, the ionsare slowed by collisions with residual molecules (the vacuum not being perfect)and trapped through the effects of the repulsion of internal walls carrying positivepotentials. Their trajectories are complex but their projections in the xy-plane,orthogonal to the field �B, correspond to a circular movement (Figure 16.13). Theradius of the circular movement depends upon the kinetic energy of the ion andis given by equation 16.2. If the velocity v is small and the magnetic field �B isintense, the circumference will be very small (less than 1 mm). From the classicexpressions v = R and = 2, relation 16.17 can be obtained. This shows thatto each mass there is a particular frequency, independent of the velocity of the ion.

Hence, at any given moment, there will be as many different frequencies ofrotation as there are ions of different m/z ratio in the trap.

m

z= eB

2(16.17)

or

= 15350Bz

m(16.18)

The practical expression 16.18 gives the frequency (in kHz) of an ion of mass m

(Da) carrying a charge z in a field �B (tesla). Mass analysis is achieved by measuringprecisely the different frequencies of the ions.

To establish the frequencies and consequently the m/z ratios of the ions, abrief pulse of RF sweep (e.g. 1 ms), commonly called a chirp, is sent, that coversa range of frequencies corresponding to the m/z values to observe. In this wayall of the ions will raise their energy. Their frequencies do not change duringthe time of the pulse, but during the irradiation pulse the radii of their trajec-tories will increase since their velocities are growing up. They describe spiralorbits. Moreover, following the impulse, the ions of the same m/z ratio cometogether, phased, which consequently induces a signal (cyclotronic resonance) ofthe same frequency, in the detector plates (Figure 16.13). Overall the ions leadto a complex signal due to the superimposition of induced frequencies by manydifferent m/z sub-populations. This interferogram, of which the intensity �I = f �t��decreases when excitation stops, contains information on each of all frequencieswhich it represents. A calculation on the data allows to extract the frequency andamplitude for each component of the composite signal [Fourier Transform of


m1

1 3

4 5

Ions m1

ν1

ν1

Output Output

Resulting vector

1

m+

vB

B

B

XYzz

F

Signal1

1 1

2

2 2

3

4

5

5 5 5

6

6 6

e–

(a) (b)

(c)

stop

Transient ioncurrent signal

RF sweepif ν1

Y

X

RF sweep ν1 − νnto accelerate the ions

2

ν1

ν3

ν2

m1

m2

m3

ν1 ν2 m2

m3

ν3m1

m3

m2ν2

ν1

ν3

ν2ν3

ν1

Figure 16.13 The principle of ICRMS. (a) Basic ion trajectory in a magnetic field takingaccount of the orientation chosen. (b) Simplified view of a ion-trapping cell (plates 5 or 6 areexcitatory, plates 3 and 4 trap the ions and plates 1 and 2 are used for detection). The ionsare formed either inside or outside the cell. (c) Principle of detection: 1, three ions waiting;2, pulse of frequency. At 1 only ion m1 is excited; 3, following excitation, ion m1 adopts awider trajectory; 4, for a real sample containing a large number of m1, these ions will arrangethemselves to orbit in phase. On detecting plates 1 and 2 they produce the effect of an electricfield vector turning at the same frequency 1 whose intensity is a function of its concentration;5, If the three ions m1 − m3 have been simultaneously excited, the signal at the exit will be aninterferogram. A Fourier calculation would lead to the usual spectrum.

I = f �t� to I = f �� or spectrum I = f �m/z�]. The main characteristics of ICRMSinclude very high mass resolution, attomole sensitivity and better than 1 ppm massaccuracy.

� All categories of mass spectrometers adopt the principle of comparativemeasurements. The instrument is calibrated with ions of known mass. Although

16.8 MASS SPECTROMETER PERFORMANCES 389

there are simple relations, some of which are included in this chapter and whichlead to the calculation of mass from a variety of parameters, they remain explanatoryformulae not used by the computer programs of spectrometers. These basic equa-tions do not take into account secondary factors characteristic to each assembly.

16.8 Mass spectrometer performances

16.8.1 Upper mass limit

All mass spectrometers can determine the m/z ratio up to a maximum value.The greatest mass, in Daltons, will depend on the number of charges z thatthe ion carries, e.g. if the spectrometer is able to measure m/z up to 2000,it will be possible to detect an ion of mass 80 kDa carrying 40 elementarycharges �q = 40e�.

16.8.2 Sensitivity

The sensitivity of a mass spectrometer is given by the weight of sample consumedper second (e.g. a few pg/s or femtomole/s) in order to obtain a signal of normali-zed intensity. Since the ion beam persists only a very short time, there is apermanent and dynamic renewal of the ions: spectra are obtained by repetitivescanning.

16.8.3 Mass resolution or resolving power

On spectra with gaussian shaped peaks (obtained with an instrument housinga magnetic sector, a time of flight or cyclotron), masses become more easilydistinguished as the corresponding neighbouring peaks become narrower. Thewidth of every mass peak is then a gauge of the performance of the instrument.This important property is at the origin of a parameter called the resolving powerR (dimensionless), for which several definitions co-exist.

To calculate R, the value m/z of the peak selected is divided by its width��m/z� either at the mid-height (full width at half maximum, FWHM) for anisolated peak, or at 5 per cent of the height when two neighbouring peaks arebeing considered (Figures 16.14 and 16.15). To be more precise, the resolution,as in most disciplines, is understood to be the smallest observable change in aquantity, here a mass interval ��m�.

R = �m/z�/��m/z� or R = M/�m (16.19)


0

50

100

5

Isotopic composition of lead

Δ(m/z)

or

Δ(m/z)

m/z203 209mass (u)

%

204 : 1,4206 : 24,1207 : 22,1208 : 52,4

A

APb

82

R = 500

Figure 16.14 Resolving power. Left, definition of this parameter in the case of an isolatedpeak. Depending upon the manufacturer the width of the peak is measured either at 50 percent or at 5 per cent of its height. Right, example of a low-resolution spectrum of a sample oflead. The value of R found depends very much on the compound and the mass chosen and ofthe slit width of the instrument.

R = 3 × 106

106.909 106.910 106.911 (u)

107Ag+R = m/Δm

R = 450

R = 1

450 452448

450 452448

Figure 16.15 Resolving power established using experimental spectra. Left, an example of arecording corresponding to a very high resolving power (ion cyclotron resonance apparatus).With this technology, which requires Fourier Transform, the theoretical maximum for resolutionwill be: R = T/2, ( being the frequency (Hz) of the ion concerned and T (s), the acquisitiontime for the interferogram). Centre, a section of a crude signal for a quadrupole mass filter�R = 450�. Right, a more conventional presentation of the same recording (resolution 1 u).

Fragmentation spectra presented in the form of lines do not permit the calcu-lation above. Furthermore it can be said that for such a spectrum the resolution(and not the resolving power) is exactly 1 u (for example distinguishing peak 28from peak 29, or peak 499 from peak 500…). In fact, with quadrupoles or iontrap instruments, this parameter is of less interest and the values of the resolvingpower are modest. An observation of the crude signal from such an instrumentshows broad peaks with flat rounded maxima (Figure 16.15). If �m is constantand close to 1 u, the resolving power will have the approximate value of the massof interest.

16.9 SAMPLE INTRODUCTION 391

16.9 Sample introduction

Given the variety of forms and the nature of possible samples, there are numerousmethods of introducing samples, each with its own particular requirements, intomass spectrometers. The sample can be ionized either before or in the ion sourceof the spectrometer.

16.9.1 Direct introduction

For gases or volatile liquids a very small quantity of sample is introduced with amicro-syringe to a kind of reservoir linked to the ionization chamber via a verynarrow channel. Under the effect of a high vacuum that is maintained in thereservoir, the compound is sucked up and vaporized. This procedure is known asa molecular leak or molecular pumping. For continuous monitoring of gases andvolatile compounds in the vapour state or dissolved in a liquid such as water, thesample can be diffused through a porous membrane.

Solid samples, able to have a sufficient vapour pressure at about 300 �C,are deposited on the tip of a metal support, which is inserted in the sourceof the instrument through a vacuum lock, then heated. For some othermodes of ionization the solid sample is mixed into a matrix (e.g. glycerol orbenzoic acid).

16.9.2 Sample introduction in hyphenated techniques

Complex mixtures of compounds are often analysed by hyphenated techniquesin which a separative method, as chromatography, is interfaced with a massspectrometer. Thus, the various constituents of the sample can be separatelyanalysed. Coupling of a gas chromatograph to a mass spectrometer (GC/MS) hasbecome widespread. The outlet of the GC capillary column is directly insertedin the ionization chamber of the MS. In this way, compounds eluting from thecolumn, mixed with the carrier gas, are introduced in the ionization chamberand then analysed in the order in which they exit the GC. As the flow rate neverexceeds 1–2 mL/min, the pumping capacity of the spectrometer is sufficient formaintaining the high vacuum required for the analysis.

Nowadays, interfacing of a liquid chromatograph or a capillary electrophoresisinstrument with a mass spectrometer is used too, although technically morecomplex. The presence of water in elution solvents is an undesirable compoundfor the mass spectrometer. With HPLC, the use of micro-columns is desirable, tohave very low flow rates. They are also well-suited with different ionization tech-niques for the analysis of high molecular-weight compounds. A rather old device,whose sensitivity is now judged to be very poor, is the particle beam interface


HPLC

Desolvatationchamber

Heating

Ionisationchamberof the MS

HeP1 P2 P3

Ions25000 500 50 (pressure, Pa)

Figure 16.16 HPLC/MS interface using a particle beam interface. Solvent molecules are lighterthan analytes, so their angular dispersion is wider. Heavier molecules, less deflected by the effectof the vacuum, have a greater probability of remaining on the axis of the system and beingtransported to the MS. This ballistic approach was much used formerly in other devices, thoughnow is all but abandoned.

(Figure 16.16) in which the liquid phase is vaporized in the form of a spray in thedesolvation chamber before entering the area where the sample is concentratedthrough evaporation.

16.10 Major vacuum ionization techniques

Analysis by mass spectrometry begins with the ionization of a compound into indi-vidual, entire or fragmented species. The choice of the ionization method dependsupon the planned study and the nature of the subject compound, which could be asmall organic molecule, a metal, a biological macromolecule…, and upon its state(gas, liquid, solid). The corresponding devices are complex and often installedduring assembling of the spectrometer, giving specialized instrumentation.

16.10.1 Electron ionization (EI)

Electron ionization is the most commonly method used for the analysis of volatilecompounds. It is the case for organic molecules. This is a ionization in the gasphase that occurs in the ion source by the collision of the neutral moleculesof the sample and electrons emitted from a filament by a thermoionic process(Figure 16.17). The ejection of the most weakly held electron leads to positiveions. This reproducible procedure facilitates the identification of a compound bycomparing its spectrum with those collected in a spectral library, assuming thecompound is registered within.

Negative ions are also formed though in smaller quantity and by differentmechanisms. Thus the technique is usually used in the positive ion mode, butthe negative ions can be also studied by inverting the polarity of the accelerating

16.10 MAJOR VACUUM IONIZATION TECHNIQUES 393

+

– – –

Ionisation chamber

Analyser

Ion beam

–100 V

Vacuum0 V

a gf

70 V

+100 V

a - Sample entranceb - Ion selectorc - Tungsten filamentd - Discharge anodee - Electron beamf - Extraction platesg - Exit slit to the MS

b

c

e

d

e–

e–

e– e–1 2 3 4

m

+.mm1

+ m1+ m2

+

m2+

–HC6H6 C6H6 C6H5 C H4 3

–C2H2

–

––

m

++

m+

m+

+

m+

m′1m′2

+++++

1

Figure 16.17 Electron ionization. The collision of an electron with a molecule m, creates aparent ion and fragment ions m+

1 and m+2 in direct succession. The neutral fragments, m′

1 andm′

2 pass undetected. An illustration for the case of benzene is shown. Below, the schematic of anionization chamber, also known as a collision chamber (or ion source). A magnetic field keepsthe electron beam focused across the ion source and onto a trap by a spiralling movement thatenhances the efficiency of this electron gun.

voltage and that of the magnet, in order to preserve the ion pathway imposed bythe instrument design.

The standard energy of ionization, usually 70 eV, is defined by the potentialdifference between the filament and the source housing. The efficiency is aboutone ion produced for every 10 000 molecules. In some cases to increase the relativeintensity of the molecular peak M , fragmentation is reduced by choosing anelectron energy close to the ionization potential of the neutral molecule, typically10–15 eV for simple organic molecules (Figure 16.18).

� A relatively explicit nomenclature is used to define the origin of the ions formed:singly monocharged, multicharged, monoatomic, polyatomic, molecular, pseudo-molecular, parent, daughter, metastable, secondary fragments, etc.

16.10.2 Chemical ionization (CI)

Chemical ionization results from the gas-phase collision between the moleculesof analyte M and the species obtained through the electron bombardment of areagent gas, such as methane, ammonia or isobutene introduced concomitantly,at a pressure of a few hundred pascals, with the compound into the ion source of


Ionisation energy: 15 eV



0

50

100

0

50

100

0

50

100

0

50

100

m/z m/z

m/z

40 50 60 70 80 90 100 110 120 130 40 50 60 70 80 90 100 110 120 130

40 50 60 70 80 90 100 110 120 130 20 60 70 100

eV

120

% Ionisation

C6H5CO2H

Figure 16.18 Influence of electron energy on fragmentation. An example with benzoic acid isshown here. A graph of the ionization efficiency as a function of electron energy is presented.Note that the spectra are normalized, that is that the most intense peak takes a value of 100.Some claim that this is an application of Procruste’s method (according to the Greek legend,the brigand Procruste forced his prisoners to lie on a bed and then, depending of their size, hewould either cut their feet or stretch their bodies so they would fit the dimensions of the bed).

the instrument. The relatively high pressure that exists in this section of the MS,reduces the mean free path of the molecules favouring collisions.

This ionization by reaction with gaseous reagents is a mild ionization procedurethat produces both positive and negative species. In particular the formation ofthe pseudomolecular MH�+ ion (which is not a radical cation) is observed, thoughits concentration depends upon the affinity of M for H+, the latter having a lessertendency to fragment than the ion M�+• obtained by electron impact. This isuseful to get the value of the molecular weight of M (Figure 16.19).

However, for compounds of type RH, the ion R+ is also observed though thechemical ionization always leaves a doubt concerning the value of the molecularmass of the compound studied.

In ammonia chemical ionization, NH4�+ behaves as CH5�+. With isobutane,the main reactive ion is �CH3�3C�+, which leads to the formation of the stableion �CH3�3C M�+, which leads to the ion �M + 1��+, and to isobutene.

16.10.3 Fast atom bombardment (FAB)

This technique of ionization and those described in the following sectionsare reserved for polar or non-volatile compounds under vacuum conditions.

16.10 MAJOR VACUUM IONIZATION TECHNIQUES 395

(Ionisation)

(Autoprotonation)

(ion at M + 1)

(ion at M + 29)

(ion at M – 1)

CH4 + e−

CH4⎤ +•

CH4⎤ +• + CH4

CH3⎤ + + CH4

CH5⎤+ + M

C2H5⎤+ + M

CH5⎤+ + RH

(CH3)3C⎤+ + M

Primary reactions:

Secondary reactions:

Collisions with M:

If M is of the type RH:

If it is a tert-butyl cation:

⎯→

⎯→

⎯→

⎯→

⎯→

⎯→

⎯→

⎯→

CH4⎤ +•

+ 2e−

CH3⎤+ + H•

CH5⎤+ + CH3•

C2H5⎤+ + H2

MH⎤+ + CH4

MC2H5⎤+

R+ + CH4 + H2

MH⎤+ + CH2=C(CH3)2

Figure 16.19 Chemical ionization. Reactions occurring with methane as reagent gas, andcollisions with the molecules M, of the compound. The last equation corresponds to that occurswhen isobutene is used. The presence of relatively heavy ions coming from the reagent gasremoves all interest in studying the spectrum below 45 Da.

Ionization is achieved through the impact of fast and non-ionized heavy atoms (Arand Xe) targeting the sample being previously dispersed in a non-volatile liquidmatrix (glycerol or diethanolamine) and deposited into the source at the end of asample probe.

To produce this fast atom bombardment a argon or xenon gas is first ionizedby electrons. These primary ions are then accelerated and directed towards acollision chamber where they come into contact with slow-moving neutrals atomsof the same gas. During those collisions, the charge of the fast moving ion istransferred to the slow-moving neutral species resulting in a fast neutral atom,which is directed at the sample (Figure 16.20). Residual ions are eliminated fromthe principal beam by deflection with an electric field. The sample, on the probe,is ionized when bombarded by the fast atom beam. This technique also causesionization of the matrix, leading to fairly large background noise, which rendersthe study of small mass ions not possible.

Instead of fast-moving atoms, fast-moving ions such as Cs+ or Ar+ can beused. This is the base of a technique called SIMS (for secondary ion mass spec-trometry). These ions, which can be accelerated, enhance the number of energeticfragmentations.

16.10.4 Matrix-assisted laser desorption ionization (MALDI)

This mode of ionization–desorption leads to weak fragmentation. The analyte tobe studied is first incorporated into a solid organic matrix (dihydroxybenzoic acid


–

–+

–

– –

–

e–

e–

e–

e–

1 2–

Xe Xe

Xe Xe+ Xe+ + Xe

Xe+

(a)

(b) Collector

Argon

Tip of sampleholder

(c)

Accelerator

Accelerating lenses

Residual ion deflector

Filament/Source

Collision chamber

Neutral argon atomIonised argon atom

Argon

Laser

TOF

+

+ –

M

++

++

++

++

–– ––

–

Laser pulses(5 ns)

Compound in the matrix

–

Figure 16.20 FAB and MALDI techniques. (a) The principle of fast-atom beam formationwith xenon; (b) The formation of fast atoms of argon in a collision chamber and subsequentbombardment of the sample by this atom beam, usually of 5–10 kV kinetic energy; (c) MALDIor ionization by effect of illumination with a beam of laser generated light onto a matrixcontaining a small proportion of analyte. The impact of the photon is comparable with that of aheavy atom. Through a mechanism, as yet not fully elucidated, desorption and photoionizationof the molecules is produced. These modes of ionization by laser firing are particularly usefulfor the study of high molecular weight compounds, especially in biochemistry, though not forroutine measurements.

for example) and next deposited upon a sample holder that is irradiated with UVlaser pulses (e.g. N2 laser, � = 337 nm, 5 ns pulse width). The laser energy strikesthe crystalline matrix to cause its excitation and the subsequent ejection of analytespecies, which are desorbed and ionized in the gaseous state (Figure 16.20c).Although a substantial amount of energy is involved, this is considered as a softionization technique.

Pulsed ionization is particularly well suited to time-of-flight instruments forbio-macromolecules, knowing that it gives ions carrying only a single charge incontrast to atmospheric pressure techniques (see following paragraph).

The analysis of small molecules �M < 500Da� is limited because the matrixdecomposes upon absorption of the laser radiation. However, other supports

16.11 ATMOSPHERIC PRESSURE IONIZATION (API) 397

based upon porous silica can be used as the matrix to overcome thisdisadvantage.

16.11 Atmospheric pressure ionization (API)

Many new applications in mass spectrometry concern either the measurement ofelements or the study of unstable and polar biomolecules �M > 2000Da�. Theseapplications have become possible with the advent of atmospheric pressure ioniza-tion (API) techniques applicable to compounds in solution following nebulization.

16.11.1 Thermal ionization (TI)

Argon plasmas are used in optical emission spectrometry (cf. section 14.3.1) toatomize and ionize elements in order to provoke the emission of characteristicspectral lines. Hence, it is not surprising that the same plasma torches are employedto ionize inorganic samples in mass spectrometry. Thermal ionization is induced athigh temperatures in a gaseous sample with microwave or an inductively coupledplasma.

The sample in solution is nebulized in the plasma generated close to a smallaperture (called a skimmer), situated axially, at the entrance to the analyser. Aproportion of the ions is sucked up due to the pressure differential (Figure 16.21).A plasma can equally be placed at the exit of a GC capillary column. Since allof the chemical bonds are destroyed in the plasma, only information concerningthe elements concentrations becomes available (for example a speciation analysisof organometallic compounds).

� Argon plasmas also contain polyatomic ions at very low concentrations, which arisefrom the air, from argon or from the sample matrix. These species can be isobaric withthe analytes ions and then could be a source of possible confusion when MS have alow resolving power. Thus if we consider N2 (28 u), O2 (32 u), ArH (78 u), ClO (51 u),ArO (56 u), CaO (56 u), the corresponding molecular ions have the same m/z ratio aselements such as Si, S, V and Fe, which could be the species under investigation. Inthis case, two methods for clarification are necessary: selection of another isotope ofthe element considered (54Fe rather than 56 Fe) or choice of another spectrometerwith a collision chamber (section 16.12) to dissociate the polyatomic ions.

16.11.2 Spray ionization

Hyphenated techniques as micro-HPLC/SM or HPCE/SM have been the drivingforce in the development of different highly sensitive devices, which have incommon the nebulization of the mobile liquid phase, issued from the separative


Skimmercone

Argon

Plasma torch

Focusing electrodes

MS (quadrupole)

Vacuum

Cr

Fe

Zn

Zn

Zn

CuZn

50 52 56 60 64 68

Sample

Nebulisatingsystem

Argon Drain

1 2 3

1 - 1000 Pa2 - 0,01 Pa3 - 0,0001 Pa

Mass (u)

Figure 16.21 Ionization in a plasma torch and recording made by the ICP/MS coupling. Aproportion of the ions generated by the horizontal plasma reaches the mass spectrometer. Below,a spectrum of a mixture of several metallic elements with masses recorded between 50 and 68 Dais shown. Note the presence of different isotopes of the elements concerned. The resolving powerof this instrument is insufficient to distinguish isobaric ions, that is resulting from differentelements yet having practically the same mass and whose signals are superimposed upon eachother in the spectrum.

instrument. Depending on the pH this mobile phase can have a variable concen-tration of H+ ions and can also contain cations such as NH+

4 , Na+, K+ (in thecase of an electrolyte).

Several techniques are available.

Electrospray or ‘ionspray’ (ESI) (Figure 16.22)

Very small droplets of solvent-containing analyte are formed at the end of a finesilica capillary whose surface has been metallized and which is hold at a highpositive potential (assuming a study of positive ions). This electric field confers alarge charge density �z/m� on these droplets. Solvent is removed through complexmechanisms, by heat or by energetic collisions with a dry gas. As the dropletsevaporate, the charge density at their surface increases leading to coulombic explo-sion (Rayleigh limit). This produces smaller droplets that can repeat the process,finally liberating non-fragmented, protonated or cationic multicharged ions of theanalyte (on average 1 elementary charge for each 1000 Da of mass). This is a soft

16.11 ATMOSPHERIC PRESSURE IONIZATION (API) 399

+

to the MS

Electrospray

HPLC or HPCE Counter electrode

+5000 V

Nebulising gas

N2

N2

N2N2

100 kPa 100 Pa 0.001 Pa

1 2 3 4

––+ +++++

–

–

–+ ++ +

+

+ +

+ +

++

+

+

+

++

+

++

+

+

+

+

++

–+ ++

++ +

++++

Analyser entrySkimmer cone

Figure 16.22 A schematic of the mechanism of ion formation in atmospheric pressure ionizationby electrospray. The analyte solution flow passes through the electrospray needle that has apotential in the range from 2.5 to 4 kV with respect to the counter electrode. The chargeddroplets have a surface charge of the same polarity to the charge on the needle. The droplets(1) shrink until they reach the point that the surface tension can no longer sustain the charge(‘Coulombic explosion’) (2) and the droplet is ripped apart, expelling analyte molecules carryingseveral charges (3). The presence of nitrogen improves the concentration process (4).

method of ionization because very little fragmentation is produced. Therefore,ESI-MS is an important technique in biological studies.

Photoionization

This mode of ionization is associated with photon induced ionization at around10 eV. In place of the corona assembly, a UV lamp is used as for the photoioniza-tion detection (cf. section 2.7.5). This process, which yields few fragments, is onlyinteresting for molecules of low polarity.

Atmospheric pressure chemical ionization (APCI)

Different from the EI source, the APCI source contains a heated vaporizer whichfacilitates rapid desolvation/vaporization of the droplets by a very brief heatingperiod up to 500 �C. Reagent ions obtained from the solvent vapour by a coronadischarge ionize the vaporized sample molecules through an ion–molecule reac-tion. Chemical ionization of sample molecules is very efficient due to the numerousion–molecule collisions (Figure 16.23). This technique leads to multicharged ionsof type �M +nH�n+ by proton transfer (in the positive mode). Unfortunately thistechnique is difficult to miniaturize as the required flow rate is higher than thatof the electrospray and as such is convenient only for volatile and thermally stablemolecules of mass less than 1000 Da.

The advantage of these soft methods of ionization is to obtain pseudomolecularand multicharged ions (z can be greater than 30), formed prior to entry intothe spectrometer. With the exception of APCI they are able to extend the range


Atmospheric pressurechemical ionisation (APCI)

HPLC or HPCE

Nebulisatingand make-up gas

N2

N2

N2

to the MS

1 2 3

N2+

N2+

Heating

Solvent molecule (e.g.,water)

Corona effectat high voltage point

+ 25000 V

Pseudomolecular ionX

x x xx

x x

M+

M+MM

xH+ xH+

Figure 16.23 Atmospheric pressure chemical ionization. (1) The sample solution is sprayed andmixed with the ions issuing from a reagent gas such as nitrogen, ionized by a polarized needle.Application of a high potential (typically ±3 to ±5kV) produces reagent ion plasma througha corona discharge, mainly from the solvent vapour. These reagent ions associate in their turnwith molecules of the analyte, leading to clusters. These are destroyed by a current of nitrogen,which mediates charge transfer to the analyte.

of masses of these intruments up to 105 Da (ex. Proteins, polysaccharides andother polymers). These procedures lead to spectra presenting the phenomenonof an ‘ionic envelope’, which leads to the calculation of the molecular mass(Figure 16.24).

M = 12360 Da

700 800 900 m/z

m/z687.5

884

773 773.25 773.50 773.75 774

Figure 16.24 Multicharged molecular ions. Left, a spectrum obtained from cytochrome C(horse heart), a protein of molecular weight 12 360 Da, by the electrospray method. Betweentwo consecutive peaks in the molecular ion cluster, the difference in the charge on the ion isone unit. The second spectrum, on the right, corresponds to the high-resolution spectrum inthe region 773–774 m/z range. From these spectra, it is possible to calculate a very close value ofthe molecular weight, as well as the number of charges carried by the ions, by two independentmethods (courtesy of McLafferty F.W. et al. Anal. Chem. 1995, 67, 3802–3805).

16.12 TANDEM MASS SPECTROMETRY (MS/MS) 401

Ionisationchamber

Quadrupole 1

Vacuum system

Quadrupole 2 Quadrupole 3Collision gas (Ar...)

Vacuum

DetectorCollisionchamber

Figure 16.25 A triple quadrupole (QQQ-MS-MS). The middle quadrupole is used as a collisionchamber. It is operated in the radiofrequency voltage mode only, where it will transmit allmasses. A gas is introduced in this middle quadrupole for collision activation. These instrumentcan conduct all three types of MS-MS analysis described below.

16.12 Tandem mass spectrometry (MS/MS)

In methods of ionization like ESI or MALDI, spectra often only contain theionized molecule with very little fragmentation data, contrary to earliest ionizationmethods like EI and CI. Consequently the spectra are of little use for structuralcharacterization. In these cases, induced fragmentation is required to complementthe measurements of mass.

Mass spectrometers have been developed with two or three mass analysers ina series to study ions fragmentation (Figure 16.25). They can be assembled indifferent configurations but all of them include a collision chamber where ionscollide with a target gas such as argon or nitrogen. The kinetic energy of ionsis converted to vibrational energy and the ions fragment (CID, collision induceddissociation). Many types of tandem mass spectrometers exist. This can be thecombination of a magnetic sector followed by a quadrupole, or two quadrupoles,or a TOF with a quadrupole (or the reverse). On the basis of data collected in afirst and normal-mode measurement, tandem mass spectrometers have differentscanning modes.

• The first method consists of choosing a precursor ion, which correspondsto a pre-selected m/z ratio with the first mass analyser, playing the roleof a filter. This ion crosses the collision chamber where it collides witha target gas as argon or nitrogen. The resulting daughter ions continuetheir course towards the second mass analyser, switched to normal mode.The m/z values of fragment ions are then determined by scanning thesecond mass analyser. It results a better knowledge of the initially selectedion, to the exclusion of the other ions formed in the ion source (daughterion scan).


• In an alternative method the second mass analyser is set to a selected m/z ratioallowing passage only to those ions, while the first mass analyser is scannedover the mass range. In this way all parent ions leading to that particularproduct ion can be identified (search for precursors).

• Finally, a double synchronized scanning of both mass analysers is made witha pre-programmed shift between them, corresponding to a given neutral mass(e.g. a neutral fragment such as CO or C2 H2). Thus, all precursor ions presentin the ion source, that undergo the same neutral loss, are detected (search forneutrals).

16.13 Ion detection

Detection in mass spectrometery is based upon the measurement of the electriccharges carried by ions. Normally the number of individual ions of the samespecies is very large and gives an analogue signal output though certain modelshave such a power of amplification that they are able to detect the impact of asingle ion.

In order to exploit a spectrum quantitatively it is essential that the number ofions detected reflects the number of ions produced, irrespective of their mass.If the mass spectra are obtained by scanning the magnetic field, the deflectionformula reveals that the m/z ratio varies with the square of the magnetic field.

Major types of detection systems:

• Electron multipliers with discrete dynodes. In this device, positive ions strikea conversion cathode-liberating electrons which are then accelerated and‘multiplied’ via a series of up to twenty dynodes (Figure 16.26). This type ofdetector is extremely sensitive, having a gain of up to 108. Aluminium-baseddynodes have improved performances of the traditional materials (Cu/Bealloys) which age rather badly in the residual atmosphere of the spectrometers,or during non-working periods (returning to atmospheric pressure).

• Continuous dynode multipliers with a channeltron®. The ions are directedtowards a collector whose entrance, in the form of a horn, is made of a leaddoped glass with which acts as the conversion cathode. The ejected electronsare attracted towards a positive electrode (Figure 16.26) and their collisionsagainst the internal walls give rise to multiplication, as with the separateddynodes. The assembly is usually mounted off-axis to avoid the impact ofneutral species as well as photons emitted by the filament, equally susceptibleto the removal of the electrons.

• Microchannel plate detectors (MCP). They consist of the union of a largenumber microchanneltrons arranged like honeycombs. This resembles anelectronic version of a photographic plate. Each individual detector is formed

16.13 ION DETECTION 403

(a)

(b)

(c) (d)

Ion

+

+

+

+

+

e– e–

e–

++

+ +

–1 kV 0 V

Multiple stage dynode detectorsingle-channel electron multiplier

Continuous dynode detectorsingle-channel electron multiplier

Electron avalanchewithin a microchannel

Microchannel plate (MCP) detector(20–100 mm diam.)

HV

Microchannel25 μm diam.

+

+

–

Low voltage

High voltage

Secondaryelectrons

1 mm

0.8–1.5 kV

Ground

Nickel-chromiuelectrodes

m

an isolated channel

ETP

e–

Figure 16.26 MS detectors. (a) Discrete dynode model with active film (reproduced courtesyof ETP Scientific Inc.); (b) Continuous dynode model. Diagram of a channeltron®: the funnelshaped cathode permits the recovery of ions issuing from different trajectories. The curvature hasthe effect of preventing the positive ions which appear by the impact of electrons on the residualmolecules and restricting therefore the production of further electrons; (c) Microchannel plate.Each plate consists of an array of tiny glass tubes. Each channel becomes a continuous dynodeelectron multiplier; (d) Details of the conversion cathode. Multiplication of the electrons in amicrotube® (from illustration by Galileo USA).


from a portion of microtube (25�m diameter) whose interior is coated by asemi-conductor material acting as a continuous dynode (Figure 16.26). Thissystem preserves the spatial resolution of the input charged ions.

� The photographic plates used in early mass spectrometers have now been aban-doned because the method was considered too slow, the emulsion having both arandom reproducibility and a non-linear response to ion current (low dynamics rangeand contrast). However the principle of simultaneous detection remains attractive.The Mattauch–Herzog type spectrographs employing ionization by sparks used thisdetection system for a long time.

Amongst the questions to be asked following this brief review of the five cate-gories of mass analysers is if analyses of the same sample compound, leads toan identical mass spectrum. In reality there is no universal analyser. Each oneof the above has its own domain. Some of these instruments analyse the ions assoon as they are formed while others begin by stocking them and absorbing theimpact of the collisions which can result in the abnormal growth of the M + 1peak. For example, magnetic sector mass analysers and TOF analysers have veryfast sampling time (nano- to microseconds) while ion traps can have samplingtimes as high as one second. For this reason mass spectrometry is held apartwhen compared with optical spectral methods which are more passive procedures.Therefore, in order to make the spectra comparable it is crucial to standardize theoperating conditions.

Applications in mass spectrometry

Mass spectrometry is one of the most dynamic sectors of the analytical instrumentationhaving innumerable applications. The technique is even now becoming essential in thefields of genomics and proteomics. The following pages show a series of applicationsof mass spectrometry used in three areas : organic analysis, elemental analysis andisotopic analysis.

16.14 Identification by means of a spectral library

Species identification through comparison of spectra is employed in numerousanalytical fields. Several software packages are used to conduct searches in spec-tral libraries in which the main peaks of known compounds are encoded. Thecompounds offering the best matches are retained as potential candidates, rankedin order of decreasing similarity with an index of 0 to 1000.

The National Institute of Standards and Technology (NIST) Mass SpectralLibrary is the most widely used mass spectral reference library, which presentlycontains a collection of about 200 000 electron impact (EI) mass spectra verified

16.15 ANALYSIS OF THE ELEMENTARY COMPOSITION OF IONS 405

by experienced mass spectrometrists plus a Kovats retention index library and aMS/MS spectral library.

Yet, when one considers the number of chemicals which is perhaps in excessof 10 million, whereas the largest of the databases of mass spectra contain some200 000 chemicals, the need to employ other techniques is obvious. In this way,and coexisting with the development of databases some software packages usethe concept of artificial intelligence methods to determine chemical structuresfrom their mass spectra. In a number of cases these techniques based uponprogrammable criteria, chemical classification of the unknown, rarity of mass etc.appear to work well, but are limited to particular classes of compounds. Theproblem lies in the fact that unknowns are more often totally unknown (such asin environmental samples).

Tandem mass spectrometry has become a tool of proteomics because it leads,in association with degradative methods, to the identification of the amino acidsequences of peptides and proteins. This is obtained by coupling a two-dimensionalelectrophoresis instrument, as a means of separation, with a MALDI-TOF massspectrometer, which produces a predominance of singly charged ions and whichfragment the peptides by cleavage of the CO-NH bond linking the different aminoacids. Although chemical or enzymatic (trypsin) protein digestion remains animportant technique for mass spectrometry, it is possible to obtain direct massmeasurements of proteins by ESI-MS.

16.15 Analysis of the elementary composition of ions

16.15.1 Methods based upon high-resolution spectra

With a mass spectrometer whose resolving power is at least 10 000, which corres-ponds to accurate masses to four or five decimal places, it is possible to find themolecular formula of parent or daughters ions. For this, the MS system presentsfor a given experimental mass, all the probable molecular formulae which couldcorrespond, taking account both of a pre-defined error window and the list of theelements supposed to be present in it (see for example, Table 16.1).

After selection of a molecular formula, the data-processing program gives thevalue of the corresponding Index of hydrogen deficiency �I�. This expresses thenumber of multiple bonds and rings in the corresponding ion (expression 16.20).If the index I is a whole number, then it is a radical cation. If I is a number plusa half, it is a cation. Generally, an ion with an odd number of electrons fragmentswith loss of a radical becoming by consequence a cation with an even number ofelectrons. Though comparatively rare these fragmentations can occur through aprocess of rearrangement and lead to a radical cation.

By associating several other considerations, such as the nitrogen rule (if thecompound contains an atom of nitrogen, its molecular mass is an odd number) or


Table 16.1 Atomic mass of the isotopes of elements commonly encountered in organiccompounds

Element Nominal mass∗ Atomic mass (g/mol) Nucleide (%) Mass (u)

Hydrogen 1 1�00794 1H�99�985� 1�0078252H�0�015� 2�014102

Carbon 12�01112 12C�98�90� 12�00000013C�1�10� 13�003355

Nitrogen 14 14�00674 14N�99�63� 14�00307415N�0�37� 15�000108

Oxygen 16 15�99940 16O�99�76� 15�99491517O�0�04� 16�99913118O�0�20� 17�999160

Fluor 19 18�99840 19F�100� 18�998403Sulfur 32 32�066 32S�95�02� 31�972071

33S�0�75� 32�97145834S�4�21� 33�967867

Chlorine 35 35�45274 35Cl�75�77� 34�96885337Cl�24�23� 36�965903

(∗) nominal mass: the integral sum of the nucleons in an atom

the isotopic composition of the elements, the nature of the principal ions presenton the spectrum can be identified.

I = 1 +[

0�5 ·i∑1

Ni�Vi − 2�

](16.20)

Ni represents the number of atoms of the element i, whose valence is Vi.

16.15.2 Method based upon isotopic abundances

This is another method to find the molecular formula of the analyte. A low-resolution mass spectrometer will suffice. As explained below, the principle isbased upon the isotopic composition of elements.

A molecular compound (which consists of an immense population of individualmolecules) gives a mass spectrum on which appears several molecular peaks(isotopic cluster at M, M + 1, M + 2, etc.), whose intensities reflect elemental andisotopic composition of the compound.

If it is known, for example, that this is an organic compound, the list of possibleelements is not too great, so, a comparison of this signal pattern with all otherpatterns of different molecular formulae, limited to those consistent with theinformation concerning the compound, allows its identification.

Consider a sample of benzene C6H6�M = 78u�. Knowing that for 100 atomsof carbon there is approximately 1 atom of 13C, it can be estimated that about 6

16.16 DETERMINATION OF MOLECULAR MASSES FROM MULTICHARGED IONS 407

per cent of the benzene molecules will include a 13C atom in their skeleton andwill therefore have a mass of 79 u (the contribution of 2H, or D, 0.01 per cent isnegligible). This explains the presence of a small peak observed at m/z= 79 in themass spectrum of benzene. Similarly, a peak will be observed at m/z = 80, dueto the presence of molecules that include either two 13C atoms or one 13C andone 2H.

Equations 16.21 and 16.22 give the relative intensities in percent of the M + 1and M + 2 peaks for organic molecules containing only the elements C, H, N,O, F, P (where nC, nN, etc. symbolize the number of atoms of carbon, nitrogen,etc.):

�M + 1�% = 1�11nC + 0�36nN (16.21)

�M + 2�% = 1�11nC�nC − 1�

200+ 0�2nO (16.22)

16.16 Determination of molecular masses frommulticharged ions

Multicharged ions are obtained from macromolecules when they are ionized inthe form of a spray (ESI, APCI). Their molecular masses can be accessed througha method alternative to that shown on Figure 16.24. A basic spectrum is requiredto undertake this calculation, which presents a succession of molecular peaksdiffering by the number of charges carried.

On the spectrum of the compound whose mass is designated by M , two succes-sive peaks M1 and M2 should be located whose charges, z1 and z2, differ by oneunit, i.e. z2 = z1 − 1 (Figure 16.27). The expressions 16.23 and 16.24 then follow:

M1 =M

z1

(16.23)

M2 =M

z2

(16.24)

Substitution and transposition leads for z1 to:

z1 = M2

M2 − M1

(16.25)

Next, knowing z1 (rounded to the next whole number) M can be calculated (Da)from 16.23.


2000 2600 m/z2800 300024002200

48+

58+

49+59

+

50+60

+

55+

72+

53+

70+

51+56

+

66+

52+

62+ 54

+

64+

57+

68+

M1M2

z2z1

Figure 16.27 Spectral profile of an antibody of high molecular mass. Multicharged ions makeaccurate mass measurements easier. This spectrum has been obtained with a ESI-MS. Not knowingthe values of the charges reported above each signal, the calculation described in the text leadsfrom M1 = 2680 and of M2 = 2729 to M = 150080Da.

16.17 Determination of isotope ratios for an element

Determination of isotopic abundance by mass spectrometry can give thegeographic source of plant-based organic compounds or mineral compounds.Using the ‘isotopic signature’ of a species leads to better precise results as thedifferent dating methodologies based upon radioactivity.

Isotope fractionation occurs during processes like evaporation or condensationand during chemical reactions. In the living world, isotopes of the same elementcan be differentiated by the biosynthetic pathways they follow. Furthermore, therate at which a molecule crosses cellular membranes will depend of the molecule’sisotopic distribution. For example, the isotopic ratio 13C/12C of natural vanillin islower than that of the synthetic vanillin; the same effect is observed for glucose,for which the isotopic distribution of carbon and oxygen varies, depending uponthe biological cycle being followed by the plant.

The detection of adulterated table oils, flavourings, fruit juices as well as studiesof plants metabolism and of numerous medical applications use isotopic abun-dance as an indicator.

To evaluate variations in the ratio 13C/12C, it is compared with an adopteduniversal standard. This reference standard is calcium carbonate from Pee Dee(PDB for Pee Dee Belemnite, USA) whose 13C abundance is very high (isotopicratio 13C/12C = 1�12372 × 10−2). Experimentally the determination is made bymeasuring the peak intensities of 13CO2 (45) and 12CO2 (44) obtained fromthe combustion of the sample. The relative deviation �, (per mL, or parts perthousand) of the compound is calculated in this way (16.26). This value of � isgenerally negative.

�0/00 = 1000

⎡⎢⎢⎣[ 13CO2

12CO2

]sam[ 13CO2

13CO2

]ref

− 1

⎤⎥⎥⎦ (16.26)

16.17 DETERMINATION OF ISOTOPE RATIOS FOR AN ELEMENT 409

In the presence of a mixture of two compounds A and B whose isotopic ratiodistributions are respectively �A and �B, the experimental value for the totalisotopic variation �M in the sample, results from the weighted combination of�A and �B. If x represents the fraction of B and �1 − x� the fraction of A, thefollowing expression allows to calculate the percentages for A and B (16.27):

�M = �1 − x��A + x��B

x = �M − �A

�B − �A

(16.27)

As this measurement involves combustion, the isotopic distribution at thedifferent sites within the compound analysed is not available. For this reason, andwhen this information is required, it is preferred to compare the D/H ratio by 2HNMR since this facilitates a comparison at each site of the molecule studied.

The determination of differences in isotopic ratios requires very precise measure-ments. The combustion step for the sample preparation is usually carried outimmediately prior to the injection into the MS. There exist instruments whichassociate in line a gas chromatograph, a tubular combustion oven, containingcopper oxide heated to 800 �C, and a low-resolution MS equipped with severalFaraday detectors, each collecting the signal corresponding to a specific mass. Acalibration compound is co-injected with the product to be studied.

� Accelerator mass spectrometry (AMS) – precise measurement of the isotopicratios of the long-lived radionuclides that occur naturally in our environment arebeyond the ability of conventional mass spectrometers. For isotopes that exist asinfinitesimal traces (a single atom in the presence of 1×1015 stable atoms) there existworldwide, a network of around 50 mass spectrometers, each derived from Van deGraaff accelerators, which are used for these analyses (Figure 16.28).

A few milligrams of a sample, which must be a solid, are first bombarded bycaesium ions. The first mass analyser extracts the negative ions corresponding to the

Injector magnet

Ion source

Tandem accelerator(Van de Graaff)

Electrostaticanalyser

Detectors

Analysingmagnet

Beam line

Figure 16.28 Accelerator mass spectrometer. The ANTARES project (Reproduced courtesy ofthe Australian Nuclear Science and Technology Organization)


pre-selected masses. Next, to eliminate interfering isobars, ions are accelerated by apotential difference of several megavolts towards the positive end of the accelerator.Along the ion beam path they collide with a target (a solid or a gas) in order that theyare stripped of electrons. Only isolated atoms, carriers of several positive charges,subsist beyond this point. These ions are reaccelerated. The gas ionization detectorscount ions one at a time as they come down the beam line. Abundance measurementsare then made by alternately recording isotopic signals arising either from the sample,the standards and the analytical blanks.

It is the chosen technique for trace level analysis as dating antique objects throughtheir 14C concentration, much more precise and sensitive than Libby’s classic methodbased upon measurements of radiocarbon activity. AMS can detect 1 14C/1015 totalions.

16.18 Fragmentation of organic ions

The manual interpretation of a mass spectrum – nature and origin of the fragmen-tation peaks – is a difficult but interesting exercise. Organic chemists are usuallyfamiliar with these methods of interpretation since they retrieve different types oftransient ions considered to explain reaction mechanisms in condensed phases.The difference here is that these ions move in a vacuum and do not collide. Thevery short period of time between ion formation and ion detection (a few �s),allows to observe the existence of very unstable species that are unstable undernormal conditions.

16.18.1 Basic rules

Fragmentation by electron bombardment, well adapted to the study of organicmolecules, results from the instability of the molecular ion formed initially. Themolecule M of which the mass is always an even number (excepting when there arean odd number of nitrogen atoms), is ionized and becomes a radical cation withan odd number of electrons represented by the symbol M�+•. For compoundsincorporating heteroatoms, ionization will preferentially occur at the heteroatomon a lone pair of electrons (Figure 16.18). At this stage, the molecule M is not yetfragmented:

M + e− → M+• + 2e−

In a second step, this resulting radical cation generally fragments. Since a massspectrum results from the fragmentation of a sample that contains billions ofmolecules, it will show all possible fragmentations. As the relative probabilitiesof fragmentation are not the same, the fragmentation peaks will have differentintensities.

Several factors control the fragmentation procedure of M�+• into daughter ionsand neutrals (radicals or molecules). Two basic situations are observed:

16.18 FRAGMENTATION OF ORGANIC IONS 411

• a cation with an odd mass number is formed (but with an even number ofelectrons), accompanied by a neutral fragment in the form of a radical

• a new radical cation appears accompanied by the loss of a neutral from M�+.

There is a greater tendency to form stable fragments (ion or neutral) andthe fragmentations with rearrangements are favoured when they involve a six-membered ring transition state leading to a hydrogen transfer at the radicalcation site.

16.18.2 Fragmentation of an ionized � bond

In a hydrocarbon such as propane, the ionization of a C—C � bond will lead tothe formation of the ethyl cation and a methyl radical rather than the reverse:

CH3CH2CH+•3 → CH3CH+

2 + CH•3

Similarly, the ionization of isobutene leads principally, by elimination of a methylradical, to the formation of an isopropyl cation which is thermodynamically morestable than the methyl cation.

16.18.3 � Fragmentation

In ketones �RCOR′�, ionization of the keto group by ejection of an electron fromone of the lone pairs of the oxygen atom (Figure 16.29) leads predominantly to thehomolytic cleavage of the C—C � bond that is in position � to the site of ioniza-tion. Elimination of the larger alkyl chain as a radical is favoured. However, in thegeneral case of a ketone RCOR′, the four fragment ions RCO�+�R’CO�+�R’�+

and R’�+ (Figure 16.29) will be observed.In ethers �ROR′� the cleavage of the C–C bond adjacent to the oxygen leads

to resonance stabilized oxonium ions (Figure 16.30). In primary amines, a similarsituation is met with formation of the iminium ion at mass 30: CH2 = NH2�+.Elsewhere, split of the ether C–O bond, leads to cations R�+ and R′�+.

16.18.4 Fragmentations with rearrangements

Besides these examples of fragmentation that occur by simple bond cleavage,ions may rearrange, sometimes by very complex pathways. Fragmentation viathe McLafferty rearrangement is a well-known transformation which occurs inmolecular ions containing a carbonyl group C=O or a double bond C=C(Figure 16.31). The reaction involves a hydrogen transfer to the initially ionization


Butanone

20

40

60

80

100

20 30 40 50 60 70 80

2927

43 43

72

57

m/z

O

CCH2

CH3H3C

O

CCH2

CH3H3C

O

CH2C

CH3H3C

O

CCH2

CH3H3C

m/z = 43

57 29 27–CO –H2

+

+

+

α Fragmentation

Figure 16.29 Electron ionization mass spectrum of butanone. The scheme explains the forma-tion of the principal ion fragments. The molecular ion leads to the acetyl ion CH3CO�+�m/z =43�, which is ten times more intense than ion 57, CH3CH2CO�+.

H2 H2

H2C

H2C

H3C

H3C

CH2

CH2CH2 CH2

CH3CH3CH2 OCH2CH3

CH3H3C H3C

H2C

CH3 CH3

H2 H2 H2H2 H2C

OC C

OC C

O

H

OH

CO

C

+

+

+

m/z = 31

m/z = 29

m/z = 59

+

+

+

+

+

+Diethylether

O

Figure 16.30 Fragmentation modes of an ether, in the case of diethylether

site (oxygen atom) which can be explained by a six-membered intermediate ring.This mechanism goes on by the elimination of a neutral ethylenic residue andformation of a new radical cation of even-numbered mass if the compound doesnot contain nitrogen.

All these transformations have led to semi-empirical rules which are used in thestudy of unknown compounds and which also are used to corroborate the resultsobtained by the automatic exploitation of spectral libraries.

16.18 FRAGMENTATION OF ORGANIC IONS 413

Butanal

20

40

60

80

100

20 30 40 50 60 70 80

2927 41

43

44

72

57

m/z

O

CC

CH

R

O

CC

CH

R

O

C

H

R

R=H, R′, OR′, OH, NHR′, X... cation-radicalcation-radical neutralresidue

+

++

McLafferty rearrangement

–CH2CH2 (m/z = 28)

O

CCH2

CH2

CH3

H

+

Figure 16.31 McLafferty’s rearrangement. Situation for butanal C4H8O

16.18.5 Metastable ion peak

Depending on the lifetime of the excited state, an ion that is formed with suffi-cient excitation may dissociate in the source giving rise to a stable daughter ionor during its flight from the ion source to the detector, giving metastable ions(Figure 16.32).

M+ → m+ + m′•

Each individual ion has a random lifetime, which usually is less than a few �s,depending upon its internal energy. This unimolecular decomposition is describedby first order kinetics. With a double focusing apparatus, a daughter ion m+ thatis formed before the exit of the electric analyser, will become lost on the internalwall of the instrument because its kinetic energy is insufficient. In contrast, ifthe decomposition occurs in the field-free region between the exit of the electricaccelerator but before the magnetic deflection, the ion that have a momentummv will be transmitted by the magnetic sector. Because its energy is less than thatof a normal ion (its velocity is less than the correct one for an ion of the samemass), the ion m+ will be observed on the normal mass spectrum as a diffusepeak situated at apparent mass m∗, which does not correspond to its real mass.The formula 16.28 relates the positions of the three signals, parent, daughter anddiffuse, on the spectrum when a metastable ion peak is present:

m∗ = m2

M(16.28)


50 60 70 80 90 100 110

105

77 –28

56.5

m/z

Field-free region

E

B

D

S

C6H5CO105

C6H577

+ CO28

++

Figure 16.32 Metastable ion peak. Theoretical aspect of the three peaks constituting themetastable transition given as an example. For the fragmentation m/z = 105 → m/z = 77 ametastable ion peak at m/z = 56�7 is observed (calcd. 56.5).

The shape of the diffuse peaks are less defined and their positions, because of themathematical relationship involved, will seldom be near by or at a entire mass(Figure 16.33). Because these peaks are wide and of low intensity, they are generallyunsuitable for analytical use except by employing special scanning modes.

Therefore through ‘peak-matching’ and metastable peak analysis, it is possibleto determine with great confidence the structure of the ions. However the latterprocedure has become a little out-dated when compared with the new and moreefficient techniques (e.g. MIKE or reversed Nier–Johnson geometry), described inspecialized monographs.

1401201008070 m/z

82

109

123

137

180

86.7 104.3

(104.3)

–28–43

180

137 109(86.7)

partial spectrum

HN

N N

N

Me

O

O Me

Figure 16.33 Metastable ions peaks observed with theobromine. The molecular ion of theo-bromine (180 Da) gives rise to an ion of mass 137 Da through loss of a CONH�• radical (43 Da).This fragmentation is accompanied by a diffuse peak at 104.3 Da. Furthermore, loss of CO (28)from the daughter ion m/z = 137 yields a second metastable ion peak which appears at mass86.7 (reproduced courtesy of Kratos).

PROBLEMS 415

Problems

16.1 The isotopic factor � of carbon, measured from the carbon dioxide resultingfrom the combustion of a natural vanillin, is �=−20. A value arising froma synthetic vanillin is �=−30. Calculate the percentage of these two specieswithin a sample of mixed vanillin, knowing that a previously measuredvalue � = −23�5 has been obtained.

16.2 To evaluate the volume of a large tank of complex shape the method ofisotopic dilution is to be used, in association with a soluble salt of lutetium.This element, which has mass M = 174�97 g/mol−1, has two stable isotopes175Lu �97�4%� and 176Lu �2�6%�. The procedure is as follows:

After filling the tank with water, 2 g of the trichloride of lutetium hexahy-drate LuCl3�6H2O, mass 389�42g/mol−1, is added.

1. What is the mass X of lutetium, introduced into the tank?After stirring until the lutetium salt is well mixed, the extractionof a sample of 1 litre of solution is taken from the tank. To thisvolume of solution is added 20�g of lutetium hexahydrate trichlorideprepared from the pure isotope 176Lu (176LuCl3�6H2O has for mass390�4g mol−1; 176Lu = 175�94g mol−1) is added to this solution.

2. Calculate the mass of 176Lu, expressed in �g, added to the sample.

3. By a classical method it is found that the ratio of the two isotopes isnow 175Lu = 90�0% and 176Lu = 10�0%. What type of apparatus wouldseem to be the best adapted to measure the ratios of isotopes?

4. Discuss the choice of lutetium for use in the experiment.

5. Finally, calculate the volume of the tank.

16.3 A magnetic sector mass spectrometer-type apparatus houses a circulartrajectory of radius 25 cm which is imposed upon the ions. The acceleratorvoltage is raised to 5000 V. A mass spectrum is recorded between 20–200 Da.

If it is assumed that each ion carries a single charge (e = 1�6 × 10−19 C,1Da = 1�66 × 10−27 kg):

1. What range of magnetic fields would be required if the acceleratingvoltage is held constant?


2. Why, in general, are recordings not made by a sweeping variation ofvoltage?

16.4 Calculate the ratio of the �M + 1�+ to M+ peak heights for footballene(formula: C60), knowing that carbon has two isotopes 12C: 12 amu (98.9%)and 13C: 13 amu (1.1%).

16.5 Vanadium (symbol V) has two isotopes whose relative abundances are51V = 99�75% and 50V = 0�25%.

To determine the vanadium concentration in a sample of steel, 2 g ofthe steel is dissolved in an acid medium and 1�g of 50V is added to theresulting solution.

After stirring, an analysis by ICP – MS is performed which obtaineda mass spectrum with two peaks centred upon the masses 50 and 51,possessing the same area size.

1. What is the % content of each isotope of vanadium in the unknownsteel if the ratio of the areas of the two peaks is the same as that ofthe masses of the two isotopes?

2. Give a more thorough answer knowing that 50V = 49�947 g/mol and51V = 50�944g/mol.

3. Explain why this problem would become more complicated if the steelcontained either titanium or chrome.

16.6 The method of isotopic labelling is employed to determine the pres-ence of traces of copper with precision. An ICP/MS installation wasemployed. The results of the experiment rely upon the ratio of theintensities of the peaks corresponding to the masses 63 and 65 of thetwo isotopes 63Cu and 65Cu of elemental copper. The experiment isdescribed below. First, a small quantity of the unknown solution wasinjected. The intensities of 63Cu and 65Cu are 82 908 and 37 092 respectively(arbitrary units).

1. Calculate the percentage of each copper isotope in this sample. Recallthat 63Cu = 62�9296g mol−1, 65Cu = 64�9278g mol−1.

PROBLEMS 417

2. The above experiment was repeated with a solution of 65Cu which wasused as an isotopic marker. For measurements a 250�L aliquot of thesolution containing 65Cu whose concentration is 16 mg/L, is added to analiquot of 250�L (approximately 250 mg), of the unknown sample solu-tion. After stirring well, the intensities of the 63Cu and 65Cu peaks weredetermined and were 31 775 and 79 325 respectively (arbitrary units).

From the above data, calculate the mass concentration of elementalcopper in the 250�L aliquot of the sample solution.Deduce the ppm copper concentration in the unknown samplesolution.

16.7 The dibenzosuberone 1 is a ketone whose structure is given below and thespectrum in Figure 16.1.

1. Calculate the exact mass from the largest molecular peak, and writethe isotopic compositions of the different species constituting peakM + 1.

2. In the mass spectrum of this compound, among other fragments, onecan see two with the same nominal mass which could represent theloss of either CO or of C2H4.

Explain the loss of CO from the parent ion and indicate if, by lossof C2H4, a positive ion, a radical or a cation-radical must result.

3. Indicate for the two peaks the corresponding molecular formula andprecise molecular weight.

4. Knowing that the resolution factor of the mass spectometer is 15 000,is it possible to distinguish the different species constituting the peakM + 1?

O

16.8 The study of macromolecules by mass spectrometry presents differenceswith respect to the studies of molecules of medium or more modest size.


1. What are these principal differences?

2. Calculate, using two different methods and the information avail-able from the recording below, an approximating molecular mass ofubiquitin (a protein found in baker’s yeast).

1 428.00 1 430.00m/z

15.65

11.74

7.82

3.91

0.001 200.0 1300.0 1400.0 1500.0

m/z

Abu

ndan

ce (

scal

ed)

17Labelling methods

Several labelling methods of analysis consist of spiking the sample with a knownquantity of a labelled (or marked) form of the analyte. After mixing the twoforms – labelled and not – a small aliquot of this new solution is withdrawn andby appropriate means it becomes possible, from the ratio of labelled to unlabelledanalyte, to calculate its initial quantity in the primary sample. This procedure iswell adapted to measure trace analytes in complex mixtures when the extractionstep is not total. Two types of labelling or marking are used, either isotopic (stableor radioactive) or enzymatic. In the latter, the compound can be isolated using animmunochemical reaction. This type of approach led to the development of radio-immunological assays (RIA, soon to be abandoned) and immunoenzymologicalassays (EIA), of which the ELISA tests are part. Although until recently the latterwere reserved for studies of biological compounds, their application to chemistryis on the increase.

Neutron activation has been included in this chapter, despite its not beingconsidered as a labelling method. This is one of the most accurate techniques foridentifying elemental abundances. This needs irradiation techniques that are notaccessible everywhere and this method has the disadvantage of causing the sampleto be slightly radioactive.

17.1 The principle of labelling methodologies

The most obvious and ideal method for the determination of the mass concen-tration of a compound in a mixture would be to totally separate it from allcomponents and weigh it. Unfortunately this can seldom be undertaken, extrac-tion being neither completely selective nor quantitative, indeed impossible if it isin a very low concentration. In this perspective, analytical chromatography of thesample, a separative method par excellence, is an indirect way to achieve extractionand to accomplish this goal. The group of methods described below stem froman entirely different principle. These other approaches are gathered under the


420 CHAPTER 17 – LABELLING METHODS

general term of labelling. To measure a particular analyte in a sample, a knownquantity of the same compound is introduced to the sample in a tagged form (e.g.labelled). This ‘tag’ allows it to be distinguished from the unlabelled form andother compounds present in the initial mixture. After allowing time for mixingand even distribution, a fraction of the sample is collected and the ratio of bothforms of the compound is used to obtain the amount initially present in thesample. The labelling of the compound must not alter its behaviour during therecovery step. This technique should not be confused with the classic methods ofstandard additions described elsewhere.

� Labelling methods are not only used in chemical analysis. To estimate, for example,the number of salmons in a pond, a definite number of fish are caught, labelledand then released again into the pond. A few days later, a number of fish (thesample) is removed and from the proportion that are labelled, an estimation of thetotal population can be deduced. For example, if after having labelled and released500 salmons and if 10 of them are found in a group of 200 fish removed a few dayslater, then the total number of salmons (x) can be estimated at 10/200 = 500/x, thusx = 10 000.

Several analytical methods have been developed from this principle. An elementor a molecule can be labelled as follows:

• By modifying the isotopic ratio of this element or one of the atoms ofthe molecule, either with a radio-element (whose activity is measured inbecquerels) or with a stable isotope (detection by mass spectrometry or NMR).These are called isotopic analyses.

• By using an enzyme or a fluorescent derivative. These are in particular,immunoenzymatic and immunochemical analyses.

17.2 Direct isotope dilution analysis with a radioactivelabel

In these types of isotopic analyses, the same compound as that to be measured isused where one of the atoms in it has been replaced by a radionuclide.

To measure a molecular compound X present in a sample, a quantity m∗S of the

labelled compound X (the reference tracer) is added to a precise quantity of thesample. The specific activity (see Section 17.5) of this tracer is represented by AS

(activity in Bq per unit of mass) while AX is the specific activity after dilution andcalculated from a very small aliquot of the spike sample isolated by a fractionationtechnique as recrystallization or chromatography

AX is smaller than AS because the quantity of m∗S (the tracer implemented) is

mixed with the quantity mX of non-labelled compound. On the other hand, theoverall activity is conserved, which is translated by the following expression:

17.3 SUBSTOICHIOMETRIC ISOTOPE DILUTION ANALYSIS 421

ASm∗S = AX�m∗

S + mX� (17.1)

The quantity mX of analyte in the sample is obtained by rearranging equation 17.1:

mX = m∗S�

AS

AX

− 1� (17.2)

If AX is much smaller than AS then 17.2 can be approximated by the followingequation:

mX � m∗S

AS

AX

(17.3)

Having calculated mX in this way and knowing the mass of sample used, it becomeseasy to deduce the concentration of X in the initial sample.

In such a procedure, the labelled tracer must be uniformly mixed in the sampleand the aliquot taken must be of a quantity sufficient to avoid weighing errors. Ifthe concentration of the compound to be measured is too low, then recovery as apure compound, even partially, could be difficult. The adaptation of this methodto very small quantities is discussed in the following paragraphs.

The preceding method is known as reversed isotope dilution analysis when thecompound to be measured is already radioactive. The principle remains the same:the activity of the subject compound (measured from a fraction), is carried outbefore and after dilution with the same compound, non-labelled. The calculationsare identical. This analysis is used for the determination of the isotopic carrier ina solution of a radionuclide using one of its stable isotopes.

17.3 Substoichiometric isotope dilution analysis

Expressions 17.2 and 17.3 suggest that in order to calculate mx it is not necessaryto know Ax and As, if their ratio is known. This observation is exploited whenthe analyte is a very small quantity and impossible to recover in its initial formby employing a traditional procedure.

The method consists in making an insoluble derivative of the analyzedcompound to isolate a part from it. To achieve this, a reproducible reaction can beconducted on the labelled standard solution (analytical blank) and, in an identicalmanner, on the sample solution in order to obtain the same recovery quantityof derivatized compound. This method, named substoichiometric, pre-dated theimmunochemical methods for trace measurement.

� For example, let us imagine measuring the quantity of sulfate ion presentat only a few per cent in an aqueous solution. After having added a knownquantity of 35SO2-

4 as the label, a solution of a barium salt (to form insolubleBaSO4) is introduced in a quantity insufficient to precipitate all of the sulfate ions.By comparing the activity of the recovered precipitate with that of the precipi-tate obtained from the same quantity of labelled sulfate alone, under identical


experimental conditions, the ratio of the activities can be deduced and conse-quently the quantity of sulfate in the original sample (this is a reverse isotopicdilution).

17.4 Radio immuno-assays (RIA)

The previous methodology, illustrated by the sulfate example, has been employedsince the 1960s for the measurement of insulin in serum. The technique, namedradio-immunology, is a transposition into immuno-chemistry of the precedingexperiment.

The basic idea is to separate, after mixing, the analyte by a means of anultraspecific reagent (an antibody), which renders possible the study of a singletype molecule amongst thousands of other substances. This approach has lead toimmuno-measurements that have benefitted enormously from the developmentof genetic engineering and biochemistry.

As in the previous method, to the sample containing the analyte, a knownquantity of this same analyte in a labelled form with a radioisotope (Figure 17.1) isintroduced as a tracer and mixed. Next, to isolate a fraction of the mixture of thetwo forms, labelled and non-labelled, a specific antibody of this analyte is addedin a substoichiometric quantity in order to have a little of the two forms. Theywill be in the same molar ratio as they are in solution. This mixture of complexeswill then be separated by precipitation before assessing its activity.

Radio-immunology has remained the method of choice for certain studies ofclinical medicine and has few applications for the measurement of molecules oflow molecular mass, because of the use of radioactive substances. Alternatively, the

+

Compound to be measuredCompound labelledby radio-isotopeOther compounds

Specific antibody

21 3 4

1 - Sample to be measured2 - Addition of the labelled compound3 - Addition of the specific antibody4 - Separation following precipitation and elimination of the undesired material

Figure 17.1 Radio-immunology testing – the different steps

17.5 MEASURING RADIOISOTOPE ACTIVITY 423

method is currently being applied to small compounds labelled with an enzyme(cf. Section 17.7), notably for applications relating to the environment.

� The methods described above, which include measurements of radioactivity, aresources of possible contamination. As such they require an appropriate environment,with the proper authorization to manipulate and handling radioactive substances.

17.5 Measuring radioisotope activity

Any radionuclide, whatever the type of radiation emitted, is characterized by itshalf-life � (Table 17.1), which is the time taken for half of corresponding atompopulation in the sample to decompose (from initial time, t = 0). Calling � theradioactive decay constant, the law of radioactivity decay allows calculation of thenumber of atoms N present after time t for a population containing N0 atomsinitially. The integrated form of this law is written as equation 17.4:

N = N0 · exp �−�t� (17.4)

with

� = ln 2/� (17.5)

Table 17.1 Some characteristics of commonly used radioisotopes

Isotope Half-life Type of emission Energy (MeV)

3H 12.26 years �− 00214C 5 730 years �− 015632P 14.3 days �− 1735S 88 days �− 0167125I 60 days IEC∗ 0149

∗Internal electron capture, Section 12.3.2.

� is in units of time−1. In practice, it is not N (the number of atoms remaining)that is known but the activity A�A=−dN/dt�, expressed in becquerels Bq (1Bq=1nuclear decay per second and 1 curie (Ci), a former unit of activity, is equal to37 × 1010 Bq). The activity, accessible through use of an appropriate detector, isdirectly related to the concentration of the radionuclide (17.6):

A = �N (17.6)

A is related to A0, the initial activity by an equation analogous to the law ofradioactive decay:

A = A0 · exp �−�t� (17.7)


17.5.1 Radioactive labelling of molecules

Only compounds for which at least one of the elements is available in a labelledform can be measured by this method. There are suppliers that specialize inthe manufacture of single-atom labelling (C, H, S …) within a relatively largenumber of organic molecules (Figure 17.2). Activity can attain 60 mCi/mmol, ifeach individual molecule contains a 14C atom at a given site. Where possible, 14Cis preferred to 3H (tritium) since the latter is easily exchanged and for which auto-radiolysis creates problems as a result of nuclear reactions between that atom and theremainder of the molecule of which it is originally a part (Szilárd–Chalmers effect).

� The isotope 14C used to prepare labelled compounds is obtained by irradiationin a nuclear reactor, of solid targets containing atoms of nitrogen (aluminium orberyllium nitride), by neutrons of low energy, known as thermal neutrons, themselvesthe product of the controlled atomic fission of 235U. The radiocarbon formed is nextisolated from the target sample by oxidation to Ba 14CO3, the variety in which itis delivered to chemists. From 14CO2, it is possible to use a plethora of organicchemical reactions to synthesize different compounds in which the radio-isotope canbe introduced to a specific position.

17.5.2 Scintillation counting

The radiation energies of the above radioisotopes are often insufficient to penetratethe window of a Geiger–Müller counter. For this reason, the compound whoseactivity is to be measured is mixed in solution with a scintillating material called ascintillator or a fluor, which transforms the � rays into a luminescence proportionalto the number of � particles emitted. The sample is diluted in a solvent (toluene,xylene, or dioxane – the latter for water-soluble compounds) that acts as a relayin the transfer of energy to the scintillation mixture comprising for example, PPO(2,5-diphenyloxazole – which emits in the UV) and POPOP emitting in the visibledomain (Figure 17.3). The quantum yield of emission depends on the energy ofthe emitted particles.

*

*

*

H

Me

Me

Me

O Me

HO

N

ON

N

N

Caffeine Cholesterol AZT

Me

Me

Me

Me

Me

H

HH

N3

N

HN

O

O

HOCH2

Figure 17.2 Three molecules labelled at a single site with 14C. This radioisotope has a sufficientlylong half-life that labelled compounds can easily be stored while avoiding corrections to takeinto account for natural decay during the measurement.

17.6 ANTIGENS AND ANTIBODIES 425

PPO

PPOexcitation 280 nm

POPOP

POPOPexcitation 300 nm

N

O

N

O

N

O

300 400 Wavelengths 500 nm

fluor

esce

nce

emis

sion

(ar

b. u

nits

)

quantum yields 0.95

Figure 17.3 Two current examples of scintillators: PPO and POPOP. Fluorescence emissionspectra of solutions in cyclohexane of these two compounds well adapted to detection withphotomultiplier tubes.

� Radioactive measurements have, of course, associated problems such as theexposure of people working with them and of the treatment of waste materials whichmeans specific risks to staff and environment. The use of tracers is therefore tightlycontrolled and possession is by licence granted following an examination of thepremises with respect to authorized ‘norms’ where such material will be stored. Theusual precautions must be taken such as working with gloves and behind a protectivescreen, using material of low activity and if possible, low energy emitters, sufficientto avoid all danger of external radiation.

From amongst the most frequently used radioisotopes only 35S emits radiation ofhigh energy. A transparent screen of lead doped plexiglass of 1 cm thickness offerssufficient protection from low activities (less than 1 MBq). However, the operator mustbe attentive to the risk of internal contamination; a radioisotope, even of weak energy,is very dangerous once it is fixed in the organism. There is no simple and directrelationship between the intensity of radiation (Bq) and the irradiation dose (Sievert).This is a function of the quantity of energy released per mass unit in the irradiatedsubstance.

17.6 Antigens and antibodies

Radio-immunological tests as well as the enzyme-linked immunosorbent assay(ELISA) which are described in the next paragraph require a brief explanation ofantibodies because chemistry and immunology are separate disciplines.

The introduction into the organism of an alien substance (antigen) of sufficientmolecular weight �M>5000Da�, provokes the production of bio-molecules called


antibodies which are glycoproteins referred as to immunoglobulins (principallyIgGs).

Antigens and antibodies, in the presence of each other, agglutinate. The forcesthat bind them are principally due to hydrogen bonding. The hydrophobic intera-ction exerted by neighbouring water molecules provokes a hydrostatic pressurethat ensures the cohesion.

The antigens induce not only an immune response but equally react with theantibodies, which are caused to appear by the living organism. However, thesetwo properties are different. Small organic molecules such as pesticides are notable of inducing a production of antibodies. In the other hand, the antigens willreact if an adapted antibody is already present: these small molecules are called thehaptens. To generate the antibodies characteristic to a hapten, the latter must beattached by a covalent bond to transporter proteins (BSA or HSA bovine or humanserum albumin), or to a polysaccharide. Therefore, the hapten must have reactivefunctionality and this structural modification must not influence the specificity ofthe antibodies that will be produced.

Polyclonal antibodies. The development of antibodies is a rather difficult work.If only a single hapten molecule was linked to a carrier protein such BSA �M =66000Da�, the antibody formed would be directed towards several sites on theprotein, called the epitotes, corresponding to sections of the protein which triggerthe production of the antibodies. Thus several tens of haptens should be bonded.Under these conditions, the antibodies obtained become specific to the haptenand not to the protein.

For this, a subcutaneous or intradermic injection is made, at different points tofive or six mice, rats or rabbits of the hapten-bound protein (immunogen) withcertain additives. This multi-point primary injection corresponds to around 100�gof pesticide. Animals having the same genetic background do not necessarilyreact in the same way. Two weeks later the same process is repeated with onefifth of the immunogen concentration. Two weeks after that, blood samples aretaken from the animals to verify if the antibodies have appeared. The injectionsare repeated two or three times in order to create hyper-immunization. Theserum of the animals is now a source of the desired antibody, which is of thepolyclonal type. By contrast, monoclonal antibodies are derived from a singlecell line.

17.7 Enzymatic-immunoassay (EIA)

Linked with the previous basic description on antibodies, there is an other formof labelling, which employs an enzyme rather than a radioisotope. In this casethe tag (the enzyme) is enormous with respect to the subject molecule. Sincethe concentrations are very low, recovery is undertaken using an antibody. Thebest known methodology of this type is the enzyme-linked immunosorbent assay

17.7 ENZYMATIC-IMMUNOASSAY (EIA) 427

- Unknown compound - Conjugated enzyme - Substrate - Chromogene

- Specific antibody - Product - Dye (colouring agent)

1 4

5

2 3

E

E

E E

EE

E

E

E E

E E

E E E

EE

S S

SS

S

S

S

C

C C

C

C

C

C

CC

C

1cm

6

P

P

P P

P

P

D

D

DD

D

D

Abs. Detection

Figure 17.4 The different steps of an enzymatic-immuno test of ELISA type with competition.In clinical analysis, there exist numerous measurements of this type. Kits are available for bothorganic and inorganic contaminants.

(ELISA) that can be done in several different ways called ‘direct’, ‘indirect’ and‘competition’ ELISA.

Over the past years, immunoassay field test kits have become a prominentfield analytical method for environmental analysis. Below is a brief outline of themethod (Figure 17.4).

17.7.1 A ‘competition’ ELISA test

1. A solution of the test sample (or of the standard or blank) is introduced inthe respective plastic tube, generally a well of a microtitre plate with have atransparent bottom for detection purposes. The walls have been sensitizedby coating them with the adapted antibodies fixed to the surface throughadsorption.

2. Aknownvolumeofa solutionof the samecompound,which is covalently linked(‘conjugated’) to an enzyme, such horseradish peroxidase, is added. During anincubation period, the two forms (labelled and not labelled) of the compoundwill enter into competition for binding with the antibodies present on thecontainer walls. Finally they are bound in the proportion of their mixture.

3. Following the incubation period (e.g. 30 min), the wells are rinsed severaltimes with water. Only bound molecules will remain in the tube. The quantityof the enzyme-linked compound fixed on the walls (to the antibody) will


be all the greater, as the amount of free unlabelled compound is low in thesample.

4. The substrate S, specific for the enzyme, as well as chromogen C designed tochange colour when acted upon by the reaction product, is now introduced.

5. The fixed enzyme will transform a large number of molecules S into speciesP, which will react with C to give a coloured product (see above). Theamplification factor imparted by the enzyme makes this assay very sensitive.The less there is of the analyte in the sample, the more there will be of thefixed enzyme and therefore the colour intensity will be stronger.

6. Finally the reaction is quenched after a short period of time by addition ofa strong acid which destroys the enzyme. The absorbance of the resultingcolour, read with a colorimeter, is inversely proportional to the amount ofanalyte in the sample.

� Horseradish peroxidase (M = 44 000 Da) is stable and reactive. The linking isobtained with four lysine residues that do not otherwise participate in its activity.According to its name, the substrate S of this enzyme is hydrogen peroxide whosedecomposition generates oxygen, which reacts with the chromogen (TMB, tetramethylbenzidine). In the presence of luminol, a chemoluminescence stable for severalminutes appears which is at the origin of extremely sensitive measurements.

This classic biological methodology is widely used in research, diagnosis, andtesting because it is affordable and sensitive to tiny amounts of material. It isapplied to domains such as the environment and agriculture (pesticides, anabolicsteroids, aflatoxins, HPA) for which numerous assay kits exist. However onlycompounds for which there exist adapted antibodies and the conjugated enzymescan be measured.

17.7.2 The relationship absorbance/concentration

The number of bonding sites on the tube wall is very small compared with thenumber of molecules in solution. Calling N the total number of anchoring sitesinside the well, n∗ the number of labelled molecules adsorbed, C∗ the concentra-tion of the labelled species in the solution and C the concentration of non-labelledunknown, we can write an expression which links the ratio R of the two concen-trations with the number of sites concerned:

n∗

N − n∗ = C∗

C= R (17.8)

The absorbance A being proportional to n∗, leads to A = kn∗, thus:

A = kN

(C∗

C + C∗

)= kN

(R

1 + R

)(17.9)

17.8 OTHER IMMUNOENZYMATIC TECHNIQUES 429

E E

E

E

E

E

in Solution

N = 8n* = 2

Lineardomain

Rel

ativ

e A

sorb

ance

(%

)R

elat

ive

Abs

orba

nce

(%)

0.1 1.0 10

log C

Analyte concentration (arbitrary units)0 10 20 30

0

20

40

60

100

80

0

20

40

60

100

80

100

Species fixed to the wall of the well

Figure 17.5 Relationship between concentration and absorbance of ELISA assays. The ratio ofthe two species in solution or fixed to the wells is the same (3, on the figure). Linearity, plottedon a semi-logarithmic scale, is only attained over a narrow range of concentrations.

A typical consequence of this relation 17.9 is the non-linearity of the experimentalcurve when the concentrations are plotted along the abscissa and at the ordinatethe percent absorbance of the solution relative to the reference obtained with theblank (C=O). This reference is obtained with the blank (all of the antibody sitesare, in this case, occupied by the conjugated enzyme).

If the concentrations are plotted on a logarithmic scale, part of the graph willbe linear to a first approximation (Figure 17.5).

The final absorbance measurement can be replaced by fluorescence detection(this is a fluorescence ELISA test). In this case the conjugated enzyme chosen isan alkaline phosphatase which converts the specific substrate into a fluorescentcompound.

17.8 Other immunoenzymatic techniques

There are several ways to conduct ELISA techniques with competition in a hetero-geneous phase medium. In one of them, the antibodies are covalently bound tomagnetic particles of 1�m diameter instead of to the container wall (Figure 17.6).This approach has the following characteristics:


Antibody attachedto magnetic support

Unknown compound

Conjugated enzyme

Magnet

21

E

E

E

E

E

E

Figure 17.6 A variant of the basic ELISA assay

• the quantity of antibodies is unlimited, in contrast to using antibody-coatedwalls

• the antibody/antigen reaction is favoured because the two partners can bebetter mixed, the medium being half-way between a homogeneous and aheterogeneous phase.

This assay is essentially the same as previously described, except that since theantibody is fixed to the magnetic particles, a magnetic field is applied after incuba-tion and before rinsing in order to maintain the antibodies against the containerwalls.

17.9 Advantages and limitations of the ELISA test inchemistry

The various ELISA assays give both semi-quantitative and reliable results morerapidly than chromatography. They are particularly practised to eliminate all ofthe non-useful negative samples, which need not be submitted to the extractionsteps and to a subsequent chromatographic analysis. There are, however, severaldisadvantages:

1. The eventual recognition of several molecules with different sensitivities cancause a dispersion in the results. There is therefore a risk of crossed-reaction(a false positive).

2. The range of measurement is relatively narrow. As the concentrationincreases, the measurement becomes less precise (an effect of using a loga-rithmic scale for the concentrations). A correct dilution for the sample mustbe found.

17.11 STABLE ISOTOPE LABELLING 431

3. The wells in microtitre plates have to contain the same quantity of antibodywith the same reactivity. This is in fact technically difficult to achieve. Theimmunization of a laboratory animal is a singular event, which explains thatresults can differ from one ELISA kit to another.

4. These kits must be stored at low temperature. They have a limited lifetime,especially for field analyses.

5. The costs of these assays with the duplicate tests and the necessary standardsmust be born in mind. They are economical only for a certain number ofanalyses.

17.10 Immunofluorescence analysis (IFA)

Labelled antibodies with a fluorescent derivative obtained from fluorescein,rhodamine or luminarin, are well suited for the measurement of a number ofhuman and animal immunoglobulins. However, the transposition of this prin-ciple to immunochemical testing for simple organic molecules remains, as yet,non-existent. There may be discrimination between the labelled and non-labelledspecies at the isolation stage for small organic molecules. This explains that onlya few examples of analysis followed by fluorescence measurement.

Several diagnostic techniques are grouped under the term of immunofluores-cence which do not correspond to measurements but rather to locate, for exampleby microscopic examination under ultraviolet light, of certain parts of the prepa-ration derived from a reaction with fluoroscein isocyanate or other fluorescentderivatives.

17.11 Stable isotope labelling

The field of application for the isotope dilution method with radioactive tags,extends to measurements using stable isotope. Mass spectrometry or nuclearmagnetic resonance are used to determine the variations in the isotopic concentra-tions. Chemical labelling using externally introduced tags consists of the additionto a sample of the same analyte but containing a stable isotope (e.g. 2H, 13C, 15N)as an internal standard. This method is as much used for molecular species as foratoms (around 60 have stable isotopes).

The reference and unknown samples differ only by the incorporation of thestable isotope. They have the same properties and behave with essentially iden-tical characteristics under any isolation or separation step. Thus the ratio betweenintensities of the pair provides an accurate measurement of the unknown concen-tration. Isotopic mass spectrometers are especially adapted for these measurements(Figure 17.7).


M = 194

O O O

O O O

CH3

CH3 CH3CH3

CD3

195 200

m/z

Caffeine Caffeine-d3

I nt.

Int.

Inte

nsity

Inte

nsity

M = 197

195 200

m/z

Time

Caffeine M = 194 u Caffeine-d3 M = 197 u 1,3-Dimethylxanthine

Peak profile at m/z = 194

Peak profile at m/z = 197

N N NN N N

N N NN N NICD3/NaOH

3 h, 25 °C

H

tR

Time

H3C H3C H3C

Figure 17.7 HPLC/MS measurement of caffeine by isotopic dilution. The stable isotope used asa tracer is deuterium D. Caffeine-d3 is a product of the methylation of 1,3-dimethylxanthineby ICD3.

Ultra-trace quantities can also be measured because, in contrast to radioactivelabelling, for which the measurement is only based upon the detection of atomswhich decompose during the time of the measurement itself; Here, all of thelabelled atoms are taken into account.

� Measuring traces of caffeine by stable isotope labelling. First a solution of thesample is made to which a known quantity of labelled caffeine-d3 is introduced. ByHPLC these 2 caffeine species have the same retention time. During their co-elution,the detector measures alternately the intensity of the peaks m/z = 194 and m/z =197. Two pseudochromatograms are thus obtained (Figure 17.7), one of peak 197the other of 194, whose areas allow the determination of the caffeine concentration.

Through synthesis it is possible to replace, in the caffeine (m = 194 u), the 3H ofthe group N-CH3 of the five-membered ring by three atoms of deuterium (D). Thisproduces labelled caffeine of mass 197 u.

17.12 Neutron activation analysis (NAA)

Activation analysis is a process useful for performing both qualitative and quan-titative multi-element analysis from almost every field of scientific or technicalinterest. The elemental concentrations in the sample are calculated following anirradiation step of the unknown sample and a comparator standard containing

17.12 NEUTRON ACTIVATION ANALYSIS (NAA) 433

a known amount of the element of interest. Neutron activation is a tech-nique comparatively easier to access than those employing charged particles.Around 60 elements can be identified and measured following their transforma-tion to radioisotopes. This particular process is part of the domain of multi-elemental nuclear activation analysis whose sensitivity varies with the element(from 1000 ppm to 1 ppb).

The nuclear reaction used for NAA is the neutron capture or �n� � reac-tion, as shown below. When a neutron interacts with the target nucleusvia a non-elastic collision, an isotope of greater mass forms in an excitedstate (Figure 17.8). By reiteration of this process, one obtains an isotopethat becomes unstable and decomposes generally by �− emission. The totalradioactivity resulting from a sample containing several elements – eachconsisting of an isotopic family – will lead of course to a complex emissionspectrum.

AZX + 1

0n −→ A+1Z X∗ �−

−→A+1Z+1Y

The total activity generated in the sample will diminish with time following adecreasing curve corresponding to an envelope of the superimposed activitiesof the individual radionuclei present. The �− spectrum being continuous, thecomposition of the elements cannot be deduced by a simple analysis of theradiation.

The key for identification comes from the emission which accompanies the�− emission and is characteristic to each radionuclide. This emission spectrumoccurs in the same spectral range as X-ray fluorescence.

γ-ray

γ-ray

γ-ray

β-particle

neutron

Target nucleus Heavier isotope

Half-life, 25 s

Radioactive isotope Product nucleus

non-elasticcollision

de-excitation

109Ag 110Ag∗ 110Ag 110Cd+ n β–

e–

+ γ (658 keV)

Figure 17.8 Schematic of neutron activation. When a neutron interacts with the target nucleusan isotope forms that can be unstable. If so, it will almost instantaneously de-excite into a morestable configuration through emission of -rays. Then, this new radioactive nucleus decays byemission of an electron and one or more characteristic -rays, at a rate according to the half-lifeof this nucleus. Illustration with Ag atom.


17.12.1 Sources of thermal neutrons

There are several types of neutron sources one can use for NAA, but megawattnuclear reactors with their intense flux of 1014 to 1016 neutrons m−2 s−1 fromuranium fission, offer the highest available sensitivities for most elements.Neutron energy distribution is quite broad, but for conventional NAA, low-energyneutrons (energies below 0.5 eV) are chosen that represent 90–95 per cent ofthe neutron flux. Sufficient levels of activation are reached in a few minutes,even if the isotope formed has a long half-life. The procedure imposes that thesample to be treated must be thermally stable. It is enclosed in a tube with acomparator standard of known concentration, before being introduced in a reactorbeam port.

Small sources of neutrons – containing an -emitter (several �g241 Amor 124Sb) encapsulated in a beryllium envelope – have been developed toavoid these restrictions. The nuclear reaction generating the neutron is thefollowing:

42He + 9

4Be −→ 126C + 1

0n

A variant consists of using a few �g of 252Cf ( –emitter, � = 26 years) as a sourceof fast neutrons (2 MeV) that are slowed by collision with hydrogen atoms. Theselow intensity radioisotopic neutron emitters (sealed devices) liberate approximatelya few hundred million neutrons per second allowing the measurement of aroundtwenty elements.

17.12.2 Detection – principle of measurement

The choice of the detection procedure depends upon the nature of the emitter andof the complexity of the emitted spectrum. The most effective solution consists ofrecording the spectrum which accompanies the majority of the �− emissions ofthe radionucleides present in the sample following activation (Figure 17.9).

The instrumentation used to measure -rays is generally a semiconductordetector (NaI(Tl) crystal) associated to a multi-channel analyser to cover energiesover the range from about 60 keV to 3.0 MeV. The functioning is similar to thatof liquid scintillators.

Introducing a time gap between the end of the irradiation and the countingstep can reduce all interferences due to short-lived emitters.

Delayed or prompt NAA. As explained above, -rays are measured at some timeafter the end of the irradiation (delayed-NAA). This is the useful method for thevast majority of elements that produce radioactive nuclides. Yet, in some cases,for elements which decay too rapidly during neutron irradiation or for elementsthat produce only stable isotopes, -rays are measured during neutron irradiation.This is called the prompt-NAA.

17.12 NEUTRON ACTIVATION ANALYSIS (NAA) 435

Cou

nts/

min

Isotopicsource

CW Agent fill

γ-ray energy (keV)C

l 195

9Cl 1

950

H 2

223

S 2

233

23001900 2000 2100 2200

Expanded spectrum of mustard gasas detected in a mortar projectile

Burster

γ -ray

Fuze

1000

2000

3000

4000

Steelenvelope

ClCH2-CH2–S–CH2-CH2Cl

252Cf

Figure 17.9 A non-conventional application of neutron activation. When it is necessary todestroy a warhead containing chemical warfare agents as mustard gas, NAA is used to identifythe contents non-destructively. This diagram, reproduced courtesy of Ametek Inc./ORTEC,illustrates the method. Right, part of the -spectrum of bis(2-chloroethyl)sulfide, that showsthe S, H and Cl signals.

17.12.3 Induced activity – irradiation time

The probability of inducing a nuclear transformation depends upon the nuclideand of the energy of the neutrons. These two factors are united in a parametercalled the effective cross-section.

The number of radioactive atoms N ∗ (the A+ 1�Z element) which accumulatein the sample during irradiation leads towards an upper limit: at each instant, theincrease in the number of nuclei N ∗ is equal to the difference between the rateof formation, considered as constant, the number of target nuclei N (the A�Zelement) being very large, and that of the rate of decay (of A + 1�Z element):

dN ∗

dt= ��N� − �� · N ∗� (17.10)

where � represents the neutron flux, � the radioactive decay-constant and � theeffective cross-section of each target atom �A�Z�. This last number is itself relatedto the mass m of the isotopic fraction f of the element �A�Z� of atomic mass M .If NA represents Avogadro’s number then:

N = �m/M�NAf (17.11)

The integrated form 17.12 of the elementary formula 17.10 allows to evaluate thenumber of atoms N ∗ present after a given irradiation time ti:

N ∗ = ��N

��1 − exp �−�ti�� (17.12)


If we consider that the induced activity measured at time t corresponds to At =�I�N ∗, with �, the detector efficiency and I the -ray abundance, then:

At = �I��N�1 − exp �−�ti�� (17.13)

The term in brackets, called the saturation factor, tends rapidly to 1 as ti increases.In this way, for tI = 6� the activity reaches 98 per cent of the limiting value.Experimentally, the time of irradiation never exceeds 4 or 5 half-lives of theradioisotope. This method cannot be used for long-lived radioisotopes. Whenirradiation stops, At begins to decrease �A = At exp �−�t��

To calculate the concentration of element X in the unknown sample �CX�, acomparator standard containing a known amount mstd of the element of interestis together irradiated in the reactor. Then the unknown sample is measured withthe same detector as the standard. Consequently, under the same conditions, thespecific activity of the unknown element X will be the same in the sample as inthe standard.

When the irradiation, decay and counting times are the same for all samplesand standards, the count rate is proportional to the mass of X in the sample �mX�,it follows that the mass of the element in the sample relative to the comparatorstandard is:

Count ratesample

Count ratestd

= mX

mstd

CX = Cstd · Wstd · Count ratesample

Wsample · Count ratestd

(17.14)

with Ci =mi/Wi where C represent the concentrations and W the masses of sampleor standard.

The relationship 17.14 is helpful if the radiation induced is simple, or when thecounting instrument is fitted with a filter permitting the isolation of the radiationfrom the element to be measured. However, often the matrix itself becomesactive and emits radiation, which comes to be superimposed upon that to beevaluated. By introducing a time gap between the end of irradiation and start ofthe measurement, the interferences caused by short-lived emitters are eliminated.

� Suppose that traces of iron are to be measured in a sample of aluminium. The59Fe (� = 46 days) is characterized by a -ray at 1.29 MeV, but during the irradiationtime, the aluminium yields 24Na, responsible for a -ray situated at 1.37 MeV, throughthe reaction 27Al(n, �24Na �� = 15 h). In order to give the short-lived aluminium todecompose, the measurements are postponed by several days.

17.12.4 NAA applications

NAA measures the total amount of an element, even in extremely low concen-trations (parts per trillion or lower), in a material without regard to chemical or

PROBLEMS 437

physical form. Samples analysed can be liquids or solids and do not have to beput in a solution.

Theoretically, every element can be neutron activated. Yet, some conditions arerequired. First, the element must have an isotope with a high cross-section thatis able to fix the incoming neutrons. Second, if delayed-NAA is used, the half-lifeof the isotope has to be long enough so the amount of activity is measurable.Third, the isotope itself must be relatively easy to get in sizeable quantities.Lastly, -rays must be produced that are reasonably intense and in a limitedenergy range.

NAA is widely used in many different fields of sciences. Applications include:environmental studies to characterize pollutants, semiconductor materials analysisto measure ultra trace-element impurities, archaeological studies of the distributionof the chemical elements and fossil materials, forensic studies as a non-destructivemethod (suspect chemical agents, see Figure 17.9), pharmaceutical materials anal-ysis to measure ultra-trace element impurities, etc. Unfortunately, facilities forusing this method do not exist everywhere. Otherwise, the sample becomes slightlyradioactive, requiring the sample to be quarantined until its activity reaches a statesimilar to which it was before the NAA.

Problems

17.1 To determine the concentration (% mass) of penicillin present in a commer-cial preparation, an isotopically labelled reference of penicillin is used,whose specific activity is 75 000 Bq/g. 10 mg of labelled penicillin is added to500 mg of sample. After mixing and equilibration, 1.5 mg of penicillin wasrecovered whose measured activity was 10 Bq. Calculate the concentration(% mass) of penicillin in the commercial preparation.

17.2 In order to measure, by isotopic dilution the mass concentration of theorthophosphate ion PO3−

4 in an aqueous solution, 3 mg of labelled phos-phate ion 32PO3−

4 (32P being a �-emitter whose half-life is 14 days), is addedto 1 g of the sample solution.

The specific activity of the added 32PO3−4 is 3100 dps/mg.

After mixing, 30 mg of orthophosphate was isolated whose overall activitywas 3000 dps. Find an expression from which the initial quantity of phos-phate ion PO3−

4 may be calculated, and calculate the % mass of this ion inthe aqueous solution.

17.3 Patulin �C6H7O4�, is a compound, dangerous to health in humans which isfound in the juice of damaged apples or grapefruits. The current method ofmeasuring this compound resembles that of a immunoenzymatic ELISA test.


A standard solution of pure patulin was prepared in water at a concentrationof 1.54 g/L just prior to use.

In the test described, four identical test tubes are used whose inner wall iscovered with a suitably adapted antibody. All of the tubes follow the sametreatment, differing only in the solution which is introduced in the initialstep. The contents are as follows:

— tube 1: a blank, 2 mL of pure water.

— tube 2: 1 mL of pure water plus 1 mL of the standard solution non-diluted.

— tube 3: 1 mL of pure water plus 1 mL of the standard solution dilutedtwice.

— tube 4: the sample, 2 mL of fruit juice, filtered and diluted twice withwater.

(In to each tube the same quantity of conjugated enzyme is introduced,plus all of the other necessary reactants combined).

Following the reaction, the measured absorbance A of the tubes wasas follows: tube 1: A = 103, tube 2: A = 047, tube 3: A = 058, tube 4:A = 05.

1. Calculate the concentration in ppm of the patulin in the standardsolution.

2. Calculate the % absorbance (also known as the % inhibition) of thesolutions in tubes 2, 3 and 4 with respect to tube 1.

3. Explain why the absorbance of tube 1 is greater than that of the othertubes.

4. Calculate the concentration of patulin in tubes 2 and 3 in �g/L.

5. Plot the calibration curve, % A = f �log C� (C = concentrations oftubes 2 and 3 in �g/L)

6. Calculate the concentration in mg/L of patulin in the fruit juice alsogiving the result in ppb.

17.4 To measure elemental chlorine present in a very weak concentration (ofthe order of a few ppm) in a sample of steel, by the method of neutron

PROBLEMS 439

activation analysis (NAA), a reactor producing a neutron flux of thermalcharacter 2 × 1016 n/m2/s is required.

1. Write clearly, using the symbols provided, the reactions taking place:

35Cl�n� �36Cl��-emitter � = 31 × 105 years�

and37Cl�n��38Cl��-emitter� � = 373 min�

2. Explain why the emissions of the isotope 38Cl are preferred for theexperiment rather than those of 36Cl.

3. Indicate two other methods which could be used to measure thechlorine in the steel. Give a precise explanation including reasons,advantages and disadvantages of the methods chosen when they arecompared to NAA.

To eliminate the interference afforded by manganese �55Mn� presentin steel which leads to 56Mn whose half-life is 2.58 hours and whoseradiation is intense, the chlorine is separated by precipitation in theform of silver chloride.

Simplified operating procedure: For five minutes and under thesame conditions in the reactor, a) a sample of the steel to be quantifiedin Cl, and b) a disc of filter paper onto which 100�L of a solution of0.1 g/L of chloride ion had been previously adsorbed, (previously it hadbeen verified that the filter paper contained no Cl), is irradiated. Thenthe steel sample is dissolved into solution by boiling with 40 mL of2M HNO3 to which is added 2.00 g of dry KCl. This resulting solutionis then introduced to 50 mL of an aqueous solution of 15% (w/v)AgNO3. The AgCl precipitate is recovered, washed and then dried.The result of the count is displayed in the following table.

Mass Mass AgCl Count (1.64 MeV) of 38Cl

Sample 0.51 g of steel 3.726 g 11 203Standard 10�g of Cl 48 600

4. Show that the silver nitrate is added in sufficient quantity.

5. Calculate the concentration of elemental chlorine in the steel sample.Recall that N = 14007, O = 16, Cl = 35453, K = 39098, and Ag =107863g/mol.

18Elemental analysis

Certain elements or compounds are more frequently measured than others.Answering to these particular needs, spectrometers and chromatographs, despitetheir obvious flexibility, are not always the best-adapted instruments for variousreasons as operation facility, rapidity of analysis, or even cost. There nowexists, alongside classic instrumentation, a whole range of ‘customized’ apparatus,possessing either modified software or material based upon the particular proper-ties of the elements or species concerned, some of them unique. The target analytesare diverse: elements, ions, molecules (sulfur, carbon, oxygen, ozone, oxides ofnitrogen, benzene, polyaromatic hydrocarbons).

These specific instrumental analyses are found in a variety of domains such asthe petrochemical industry, metallurgy, agriculture and the sectors of atmosphericpollution, soils and water sectors, the detection of chemical weapons, the fightagainst terrorism and other areas. These instrumentation of specific analysersshould not be neglected. This chapter reviews several original methods limited tosingle elements only.

18.1 Particular analyses

When hundreds of analyses per day must be undertaken, traditional laboratorymethods and instruments can be less effective (e.g. data throughput too slow or toomuch data to be treated). Therefore there are other instruments for these singularapplications which correspond to integrated systems for obtaining more quicklyinformation concerning the concentration of particular elements or compounds.For example, finding out the carbon, hydrogen, nitrogen, oxygen content ofunknowns is one need in organic chemistry research. One other area for whichthere is an increasing requirement is that of continuous systems analysis, whichhas for objective automation and control in real time, of numerous industrialmanufacturing procedures. Amongst the species imposing the most attention are


442 CHAPTER 18 – ELEMENTAL ANALYSIS

atoms and molecules. To illustrate these aspects, some methods are described inthis chapter.

18.2 Elemental organic microanalysis

The very great number of molecular compounds containing carbon (C) andsome other light elements such as hydrogen (H), nitrogen (N) and oxygen (O)have provided the need to measure these elements for a wide range of research,industrial and academic applications. The biosphere uses three or four elementcombinations as varied as and perhaps more varied than those that form themineral kingdom. A multiplicity of sectors (petrochemicals, pharmaceuticals, oragrochemicals) in organic chemistry are concerned.

When molecules are synthesized by multi-step sequences or when newcompounds are extracted from natural sources, their structure and purity mustbe elucidated. For this, a quantitative elemental analysis must be performed. Thisparticular type of analysis allows us to find the percent elemental composition,in the pure state, of the molecule under study. The measurement of a singleelement, indeed two (C and H are the most frequent) will verify the accuracy ofthe molecular formula proposed for a molecule not as yet fully defined but forwhich a structure has been deduced from spectral studies. Elsewhere, purity of acompound for which the composition and the molecular weight are known, canbe determined by comparison of the experimental results obtained from a samplewith the theoretical ones (Figure 18.1).

For such light elements, atomic absorption spectroscopy (unusable due to alack of suitable sources) or of X-ray fluorescence spectroscopy (lack of sensitivitydue to radiation of low energy) are inappropriate.

The principle applied for measuring these elements is to burn a small sample(a few milligrams) of the compound by rising it to a high temperature in thepresence of oxygen, with customized analysers. The elements H, C, N, O, S arerecovered in the form of gaseous oxidation products. This also has the advantageof separating them physically from the matrix.

� Elemental microanalysis gives essential information, though insufficient todeduce the molecular formula for a totally unknown compound. Even if all of theelements present had been measured, which is never the case as instrumentsare designed to determine only a few ones, the molecular formula is known,but not the molecular weight. Taking as an example the results shown onFigure 18.1, the molecular formula C54H54N6O12S2 would have the same percentage

C27H27N3O6S requires % C 62.18 H 5.22 N 8.06

M = 521.5 g/mol found % C 62.02 H 5.29 N 8.15

Figure 18.1 Conventional presentation of an elemental analysis for an organic compound

18.2 ELEMENTAL ORGANIC MICROANALYSIS 443

composition in elements than C27H27N3O6S. In the majority of cases mass spec-trometry, or NMR, is called upon to remove this ambiguity and determine the correctformula. Finally, it should be noted that for all compounds the percentage analysis,despite its inherent experimental error, will, when combined to a mass determinationmethod, find the exact molecular weight and formula, the number of atoms beingalways an integer.

18.2.1 Traditional methods of Dumas and Pregl

Current elemental analytical methods are based on the combustion of a knownamount of the sample using a modified Pregl–Dumas technique. To find the atomiccomposition of an organic compound, a sample is weighed in a consumable tincapsule, then injected into a high temperature furnace and combusted in an excessof pure oxygen. If the elements C, H and N are present, the resulting combustionproducts, carbon dioxide �CO2�, water �H2O� and a mixture of nitrogen andnitrogen oxides �N2 + NOx� will be formed. The amounts of these gas lead bycalculation to the percentage of the elements in the initial sample. Elementaloxygen is determined separately by combustion in the presence of carbon to formcarbon monoxide.

� Historically, Dumas founded a new analysis method when he developed in the1830s, a procedure for estimating the amount of nitrogen in an organic compound.But it is Pregl, Nobel Prize laureate in Chemistry ‘for his invention of the method ofmicroanalysis of organic substances’ who was the precursor of today’s instrumenta-tion. Pregl was able to make measurements of carbon, hydrogen, nitrogen, sulfur,and halogen, using only 3–5 mg of starting materials with results as accurate as thoseobtained by macroanalysis.

In the early microanalysis apparatus developed by Pregl for carbon andhydrogen, the combustion was made at 750 �C in a current of oxygen, the trans-formation of CO into CO2 being completed by passage over a mixture of copperoxide and lead chromate (Figure 18.2). The masses of elements C and H werecalculated from the increase in weight of two tubes (previously weighed), onecontaining magnesium perchlorate (for H2O) and the other quicklime (for CO2):precision reached 0.1 per cent providing the balance could measure in mg.

Later a second generation of analysers were developed (Figure 18.2), whichincorporated specialized reagents to remove interferences including halogens,sulfur and phosphorus. The gases are then passed over copper powder to eliminateexcess oxygen and reduce oxides of nitrogen to elemental nitrogen. In these CHNanalysers, to simplify the operation, the double weighing is replaced by measure-ments of thermal conductivity differences in gas mixtures before and after passagethrough two selective traps, the first of which is a water trap (H determination)and the second one for carbon dioxide (C determination). Finally, nitrogen ismeasured against a helium reference.


Oxygen Helium Mg(ClO4)2M

g(C

lO4)

2NaOH/Ca(OH)2

NaO

H/C

a(O

H) 2

Preweight tubes(gravimetric technique)

O2

O2 CuO/PbCrO4

Oven

CH-Analyser, historic Pregl apparatus

CHN-Analyser, Simon apparatus

Absorption

Absorption

He

–H2O

–H2O

H2O

–CO2

CO2

–CO2

PbO2

Cu

Reduction

Oxidation

Mobile oven

Combustion zone

N2

+He

N2

Mixing Ballastvolume

AgVO3/Ag2WO4

750°C 200°C

TCD1H

TCD2C

TCD3N

ExhaustHe

Figure 18.2 Pregl method of microanalysis. Generations of students will recall having calcu-lated, with anxiety, molecular formulae from the masses of carbon dioxide and water trapped inthe removable absorbers. In a more recent version, the reaction gases pass over copper powderto reduce the nitrogen oxides to nitrogen. Three thermal conductivity detectors (TCD) signalthe presence of H2O�CO2 and N2. The measurement of the three requires elements requirearound 10 minutes.

18.2.2 Current elemental organic analysers CHNS-O

Other modern analysers keep the sample combustion principle, but the formedgases are measured by a chromatographic method (Figure 18.3). About 1 mg ofthe sample is pyrolized at 900 �C in the reactor chamber in the presence of anoxygen excess. The complete oxidation is reached on a tungsten trioxide catalyst.The leaving gas stream includes carbon dioxide, water, nitrogen oxides and anexcess of oxygen. The product gas mixture flows through a silica tube packedwith copper granules where excess oxygen is fixed and nitrogen oxides reduced togaseous nitrogen. Finally, the gas mixture is brought to a defined pressure/volumestate and is passed to a gas chromatographic system. The elements N, C, H are atthe origin of three compounds in the gas state, N2, CO2 and H2O, separable bya packed GC column associated with a thermal conductivity detector. Oxygen inthe sample is measured separately, as carbon dioxide, obtained by pyrolysis in thepresence of platinized carbon, and of course, in the absence of oxygen.

18.3 TOTAL NITROGEN ANALYSERS (TN) 445

He

GPC columnTCD

HeO2

Combustion(1800°C)

Oxidation

Reduction(500°C)

Nitrogen

Carbon dioxide

Water

Sulfur dioxideSample

N H SC

Figure 18.3 Microanalysis apparatus with chromatographic detection. The Porapak filledcolumn separates the four gaseous components carried away by the helium carrier gas. Througha prior calibration with standards, the concentration of each of the 4 elements in the samplecan be deduced from the areas of the corresponding peaks on the chromatogram.

18.3 Total nitrogen analysers (TN)

The total nitrogen content is used to characterize numerous products andsamples in the petrol, paper and carbon industries. These measurements canbe carried out with CHN analysers as described previously, but to simplify theprocedure, customized analysers have been developed for this single element.They are an alternative for cumbersome reference methods, such as totalKjeldahl nitrogen (TKN – corresponds to the sum of organic nitrogen andammonia).

In the Kjeldahl method the compound containing the nitrogen is first digestedin sulfuric acid in the presence of a catalyst before being taken up by a mixture ofsodium hydroxide, sodium oxide and calcium hydroxide in order to transform thenitrogen within the substance to a single ammonia-based solution. This sequenceends by taking up this solution in water vapour to remove the ammonia formed,which is finally measured by acidimetry. This method can be rendered semi-automatic but it suffers the inconvenience of using inherent corrosive reagentsand titrated solutions as well as being rather time consuming.

After pyrolysis and reduction, the gas mixture containing nitrogen passesthrough a trap to remove water and the combustion gases (Figure 18.4). Thegeneral detection procedure, based on the thermal conductivity of the gas, isreplaced by specialized detectors based on the chemiluminescence of nitric oxide(NO) when combined with ozone �O3� (cf. Section 11.8).

NO + O3 → O2 + N∗2 → NO2 + h�


Oxidation Reduction Absorption

Flash dynamiccombustion T = 1800 °C

He

N2

GC column

TCD

HeO2

Combustion(1800°C)

Encapsulatedsample

– CO2

He

He + N2

CO2

H2O

N2

– H2O

Reduced copper

Time

Sig

nal

Figure 18.4 Instrument for nitrogen analysis. This instrument is a modern adaptation of theDumas’ method, with the conventional detection by means of a catharometer (He is thecarrier gas).

or upon the oxidation of NO in contact with an electrochemical sensor (cf.Chapter 20):

NO + 2H2O → HNO3 + 3H+ + 3e−

� In Dumas’ original method (1840) the substance was heated with copper oxidein an atmosphere of carbon dioxide. Elemental nitrogen was partially oxidized tonitrogen oxides NOx, which were subsequently reduced over copper. The nitrogenpercentage was calculated from the volume of the gas released, measured with agraduated test tube.

Figure 18.5 A total nitrogen analyser – model TKN, reproduced courtesy of Skalar. Detectionby chemifluminescence. The small amount of light is quantified and is proportional to thenitrogen content of the sample. This type of instrument can be used for measuring proteins.

18.5 TOTAL CARBON ANALYSERS (TC, TIC AND TOC) 447

An example of application can be seen in food-processing industrywhere the measurement of the total nitrogen content has been adopted bynumerous countries as the reference for calculating the protein concentra-tions, generally accepted as corresponding to 6.5 times the nitrogen value(Figure 18.5).

18.4 Total sulfur analysers

Sulfur content is often measured for industrial controls by X-ray fluorescencebecause the samples usually form part of a series, which may be compared withvery similar standards. Yet, for organically bound sulfur compounds that can bedestroyed by combustion in a current of oxygen, the measure is based upon thevolume of sulfur dioxide �SO2� formed in an instrument similar to that describedpreviously. Three main procedures of quantification co-exist with which the othergases of combustion do not interfere:

• Detection of sulfur dioxide by fluorescence, a process that can be summarizedas follows:

SO2 + h� → SO∗2 → SO2 + h�

• Specific action of iodine on SO2 in the presence of water, a reactionexploited elsewhere for the measurement of water by the Karl Fischer method(Chapter 20). The instrument gives the minimum quantity of current requiredto be generated in a coulometric cell, by an electrolyte containing an iodide,in order to oxidize SO2. If it is known that 2 electrons are required to oxidizea molecule of SO2, one sulfur atom will correspond to 2 × 1�6 × 10−19 C.

• Oxidation reaction of sulfur dioxide in nitric acid, in contact with the workingelectrode of an amperometric cell (cf. Chapter 20):

SO2 + 2H2O → H2SO4 + 2H+ + 2e−

18.5 Total carbon analysers (TC, TIC and TOC)

With the previous combustion method, analysis is performed when carboncompounds are combusted in an oxygen-rich environment, resulting in thecomplete conversion of carbon to carbon dioxide. This procedure is not appli-cable to water samples with a very low concentration in elemental carbon as usedfor semiconductor manufacturing processes or required in pharmaceutical indus-tries. For these cases the organic contaminants are measured by the total carbon


content in water, expressed as the sum of the carbon contained in different organicfractions defined as follows:

• total inorganic carbon (TIC) – the sum of inorganic carbon species in a solution(carbon dioxide, carbonic acid, hydrogenocarbonate anion, and carbonateanion) dissolved in the aqueous sample

• total organic carbon (TOC) – the amount of carbon covalently bonded inorganic molecules

• total carbon (TC) – represents the amount of elemental carbon in the sample.

Appropriate analytical methods must be used to measure these three fractionsof the total carbon content.

The TIC is available through a coulometric detector. To determine the TOC,all recent analysers employ the same basic technique. The first stage of themethod is the removal of the inorganic carbon with an acid such as H3PO4

(the TIC being essentially in the form of carbonates) introduced in the liquidsample. Thus the inorganic carbon is converted into carbon dioxide gas thatis stripped out of the liquid by a carrier gas. The remaining organic carbon isthen oxidized by UV radiation and carbon dioxide generated from the oxida-tion process is subjected to a conductimetric detection in a conductivity cell(Figure 18.6).

Sampleinlet

Sampleinlet

UV Oxidation reactor

UV oxidation reactor

Conductivity cell

Conductivity cell

TOC value

TOC value

to wasteto waste

H2O

H2O

H2O

H2O

CO2

CO2

HCO3–

Cl–

etc..H+

CO

2

CO2 transfer moduleC

O2

rem

oval

Direct detector Membrane detector(a) (b)

UV

Figure 18.6 Direct and membrane conductimetric detection methods for measuring TOC.Radiation of a high output UV lamp (185 and 254 nm) produce, in water, by differentpathways, hydroxyl free radicals (OH), which oxidize the organic compounds to carbon dioxideand water from oxygen dissolved in the water. The difference between types (a) and (b) detectorsis that the direct detector is subjected to interference from ionic contamination, acids, bases,and halogenated organics. In the membrane based conductimetric method, the membrane is aprotective barrier to interfering ions, enabling the analysis of CO2 only (reproduced courtesyof GE Analytical Instruments for illustrations).

18.5 TOTAL CARBON ANALYSERS (TC, TIC AND TOC) 449

Drying tube

PMT

Cell (silica glass)Hg lamp

Hg lamp

Beam splitter

Lamp control detector

Analog-digitalconverter

EDL

EDL

HFSample

InOut

Cold-vapour atomic fluorescence spectroscopy

Cold-vapour atomic absorption spectroscopy

Sample air

Carrier gas

Zero air

Cartridge assemblyamalgamation & desorption

Detector

Sample pump

Pump exhaust

Cell ventCell

Flow meter

UV

EDL

Atomic fluorescence

Atomic absorption

Sample in/out

Int.

Int.

.

·

Figure 18.7 Mercury analysis. Two models of analyzers (Reproduced courtesy of MercuryInstr. USA and Genesis Laboratory Systems Inc.). The mercury concentration is measured in anoptical cell made of fused silica on the path of a mercury discharge lamp(253.7 nm resonanceline). Mercury is measured either by AAS or FAS.


18.6 Mercury analysers

Mercury, a heavy metal, is a dangerous pollutant because of the ease with whichit may give highly toxic organic derivatives such as dimethylmercury. It is presentin a wide variety of sample matrices including water, wastewater or soils andin many sites from chlorine-alkali plants to waste incinerators. The analyticalmethod must be highly sensitive because the gaseous or aqueous samples containmercury concentrations that may be many orders of magnitude less than possibleinterfering compounds.

� The power plants burning coal and municipal waste incinerators are sourcesof mercury pollution. During thermal processes, all mercury is first converted intoelemental form, but during cooling different derivatives can be formed, according tothe matrix composition of the flue gas.

To be detectable, mercury must be present in elemental form. Thus for gaseoussamples a thermal conditioner unit converts, in the presence of a catalyst, allmercury species present in the sample into elemental form. For liquid samples aspolluted water, a first treatment by an acidic oxidizing mixture exchanges mercurycompounds into Hg(II) ions that are then reduced to elemental mercury with atin salt.

When atmospheric mercury is to be measured, the mercury is preconcentratedby passing the sample through a trap containing gold-coated sand. This goldamalgamation enhances detection limits. The amalgam is next heated to desorbthe mercury that is detected and measured either by AAS for concentrations within

Sample

b

a

a

Gas/liquidseparator Detector

Pumps

a Sheath gas (Ar)b Sample in

Reaction cell

to Waste

Hg lamp

PMT

NaBH4

Blank

Arg

on

b

Figure 18.8 Mercury analysis by cold vapour atomic fluorescence spectrophotometry (CVAFS).Measuring principle. (Model reproduced courtesy of P.S. Analytical). The fluorescence ismeasured at 90 � with respect to the incident direction by a photomultiplier tube.

PROBLEMS 451

10 ppt to 10 ppm (Figure 18.7) or by atomic fluorescence spectrometry (CVAFS)at ppt or sub-ppt level (Figure 18.8). The last method is less vulnerable to falsepositive responses and has a better linearity.

Problems

18.1 Analysis of an organic compound has revealed that it contains only carbon,hydrogen and oxygen. From the combustion, in a Pregl apparatus, of5.28 mg of this compound, 10.56 mg of carbon dioxide and 4.32 mg of waterare obtained.

What is the molecular formula of the compound knowing that massspectrometry reveals no significant peaks above m/z = 89?

Given: M(C) = 12 g/mol; M(O) = 16 g/mol; M(H) = 1 g/mol

18.2 An analyzer based upon AAS and containing a tin chloride elemental reduc-tion device is employed to measure the mercury in an industrial waste watersample. The cold vapour mode is used. Three standard solutions and thesolution of the sample to be measured give the following results:

Solutions conc.(ppb) Signal (muA.s)∗

Standard 1 0.02 16.66Standard 2 0.05 42.52Standard 3 0.2 171.2Sample ? 48.25

(∗) integration of the absorbance signal as a func-tion of time.

1. Indicate the principal advantage and the principal disadvantage of thismethod.

2. Calculate the concentration (ppb) of mercury in the sample solution.

19Potentiometric methods

A great deal of quantitative measurements in chemical analyses are based onelectrochemistry. Called electrochemical methods, they can be separated into twocategories: those based upon measurements of potentials (potentiometry) andthose which exploit measurements of current (voltammetry).

The first group, which is developed in this chapter, use ion selective electrodes(ISE). The principle of these chemical sensors is to create an electric cell in whichthe analyte behaves in such a way that the potential difference obtained relates to itsconcentration. Measurement of pH, probably the most common and best knownelectroanalytical method, is part of this group. Most of the measurements concernthe determination of ions in aqueous solution, though particular electrodes withselective membranes also allow the determination of molecules. The sensitivity ofthese methods is very great for certain ions but matrix is sometime responsiblefor lack of reliability in these measurements. In such cases, complexometric ortitrimetric methods must replace direct potentiometry. It remains however forpotentiometry multiple applications in which the instruments range from low-costpH meters to automatic titrators.

19.1 General principles

Potentiometric measurements are based upon the determination of the voltagedifference, at zero current, i.e. under equilibrium conditions, between two elec-trodes which are plunged into a sample solution (Figure 19.1). Each of theseelectrodes constitutes a half-cell. The following concerning these two electrodesshould be noted:

• The external reference electrode (ERE), is the electrochemical reference half-cellfor which the potential is constant with respect to that of the sample solution.

• The ion selective electrode (ISE), also known as the working electrode, iscomposed of an internal reference electrode (IRE) bathed in a reference solu-tion of the analyte i subject of the measurement. The electrode, which is


454 CHAPTER 19 – POTENTIOMETRIC METHODS

used for measurement, is separated from the sample solution by a membrane,selectively permeable to the analyte being studied. The measuring sequenceis then as follows:

IRE/internal solution/ion-selective membrane/sample solution/liquid junc-tion/ERE

For studies in aqueous solutions, the external reference electrode (ERE) is oftenan Ag/AgCl/KCl electrode, made of a silver thread covered with silver chloridebathed in a solution of potassium chloride. Electrical contact with the solutionunder study is achieved through a finely porous fritted glass. Since the ions havea tendency to migrate across the membrane, there is a resulting low potentialjunction EJ that can be minimized by a salt bridge, usually a saturated solution ofpotassium chloride.

The potential difference (PD) between the IRE and the internal membranesurface is constant, as fixed by its design (e.g. the nature of the reference electrodeand the activity ai�reference of the reference solution). Alternatively, the PD, whichappears between the external surface of the membrane and the sample solution�Ememb�, depends upon the activity of the target ion �ai�solution�. The potentialdifference across the membrane is described by the Nernst equation:

Ememb = 2�303RT

zFlog

ai�solution

ai�reference

External reference electrodeIon selective electrode

Ag/AgCl Ag/AgCl + specific ion i

Filling port

Sample solution

Diaphragm Membrane

EERE EERE

EJ

Internal solution

The membrane is permeable to the selective ion

Ememb.

EIRE

EIRE

ERE

ERE

ISE

ISE

Junction potential

External referenceelectrode potential

Internal reference electrodepotential with respect tointerior buffer

Global potential of the membrane

mV

EmembraneEJ

ci

Figure 19.1 Measurement set-up of an ion selective electrode (ISE). The potential of themembrane permeable to the ion varies with the concentration of the specific ion in the solu-tion sample. The measured signal is the sum of different potentials generated at all interfaces.Measurements are typically conducted by an ionometer. They are made at zero current. Underthe equilibrium conditions the transfer of ions from the membrane into solution is equal to thetransfer from the solution to the membrane. Manufacturers also supply more robust electrodescalled combined electrodes, that include both external and ion selective electrodes in the samedevice. pH electrodes are of this type. Unfortunately the schematics are less clear due to thecompact arrangement.

19.2 A PARTICULAR ISE: THE PH ELECTRODE 455

The cell potential is measured as Ecell = EISE − EERE + Ej

Such as Ecell = EIRE + Ememb − EERE + Ej

The terms EIRE and EERE are independent of the concentration Ci of analyte i.They have no reason to vary during the measurement. Therefore the potential ofthe cell depends upon that of the membrane (EJ is minimized as explained above).

The activity of the target ion being kept constant inside the electrode �ai�reference�and provided the membrane is only permeable to this single type of ion, the PD,i.e. the electromotive force, is linked to the activity ai of the ionic species i in thesample solution, by the equation:

Ecell = E′ + 2�303RT

zFlog ai�solution (19.1)

In this Nernst-type equation, E′ is the standard potential of the measuringsequence used. It takes account of all other potentials. R is the ideal gas constant,F represents Faraday’s constant (96 485 C), T is the temperature, z is the chargecarried by the target ion i to be measured (indicating whether + or −) whoseactivity is ai and 2.303 is the logarithmic conversion factor.

The activity ai of an ion i is linked to its concentration Ci by the relationshipai = �iCi where �i is the activity coefficient which depends on the total ionicstrength I , that is a measure of the quantity of charge of all ions present in themedium �I = 0�5�Ciz

2i �. For example, for an ion i, of charge z, expression 19.1

becomes:

Ecell = E′ + 2�303RT

zFlog �iCi (19.2)

For diluted solutions, the Debye–Hückel law – log �I =−0�5z2i

√I – indicates that

for a given value of I , �i is constant. This is why the same quantity of an inertelectrolyte, called ‘support electrolyte is added to the range of standard and samplesolutions’, in order to have a large excess of indifferent ions, which stabilize theionic strength at a constant value. This ISAB (ionic strength adjustment buffer)or TISAB (for total ISAB), limits variations in �i. Under these conditions, themeasured potential difference depends on the concentration of the ions to beanalysed and is given by equation 19.3, which results from equation 19.2:

Ecell = E′′ + 2�303RT

zFlog Ci (19.3)

19.2 A particular ISE: the pH electrode

This electrode, also called the glass electrode, is specific to H+ ions and highlyselective. Glass in this case does not refer to the material of the electrode (whichcould equally be of plastic), but refers to the membrane that ensures contact


with the solution. This membrane is composed of a thin wall of special glass thathas a high sodium concentration (25 per cent). Its surface becomes hydrated inthe presence of water and is comparable to a gel, while its inside corresponds to asolid electrolyte. On a microscopic scale this glass is an orthosilicate network withanionic fixed sites and cationic vacancies. This salt of orthosilicic acid Si�OH�4 hasan open structure with sodium cations that allow the transfer of charges from oneside of the membrane to the other (Figure 19.2). The outside of the membrane isin contact with the sample solution while the inside is in contact with the internalelectrolyte which has a constant acidity (ca� pH 7). In short, the membrane is theseat of exchange between cations Na+ and H+:

H+�solution� + Na+�glass��Na+�solution� + H+�glass�

When the H+ concentration is different on either side of the membrane, a potentialdifference PD will appear between them, which is related to the activity of H+ ions

IRE ERE

a Glass pH electrode

Glass membrane

H+ ions

Oxygen atomsNa+

ionsSilicon atoms

Electrolyte junction

(H3O+ = a1)

a1

Solidelectrolyte

a2 a1

Interface

Ag/AgCl

Ag coveredwith AgClAgCl

KCl 3 M

Glass membranesensitive to pH

ERE IRE

KCl andHCl 4 Ma2

Junction(diaphragm)

Filling

mVGlass electrode Sample

solution

AgCl/Ag [Cl] = 4 M Ag/AgCl sat. and KCl(H3O+ = a2)

Figure 19.2 Glass electrode for measuring pH. The concentration of H+ ions is accessiblethrough the potential difference which appears between the glass electrode and the externalreference electrode (here an Ag/AgCl electrode). Above, a cross-section of the membrane perme-able to H+ ions. When an H+ ion forms a silanol bond, a sodium ion moves into solution topreserve electroneutrality of the membrane. Two processes occur: ion-exchange and diffusion.Below left, a cross-section of a combined electrode in a concentric arrangement, where thereference electrode surrounds the glass electrode. The junction permits the migration of ionssince the liquids from each side should not mix. Prior to its use, the pH-meter is calibratedwith a buffer solution of known pH.

19.3 OTHER ION SELECTIVE ELECTRODES 457

in solution, i.e. its pH. This later is determined by an electronic millivoltmeter,the pH-meter, which monitors the PD between the glass electrode and an externalreference electrode ERE. The instrument, after calibration, calculates directly thepH of the solution. For environmental reasons Ag/AgCl electrode is preferred overthat of calomel (mercurous chloride/Hg).

19.3 Other ion selective electrodes

During the early days of potentiometry, it was noted that interferences couldoccur and affect pH value, depending upon the composition of the glass usedfor the membrane, principally if other alkaline ions were present besides sodiumion. This is known as the alkaline error, which occurs for pH above 13. This ledto the development of glasses that could respond selectively to monovalent ionssuch as Na+�K+�Li+ and Ag+. Selectivity depends on the material that servesto ensure contact between the solution to be analysed and the inside of theelectrode, but a membrane truly selective for a single type of an ion does notexist. In all cases an ionic material is required that will permit the establishment ofconcentration equilibrium for a specific ion. A PD will appear if the activity (or theconcentration) is different between the two faces of the membrane. Measurementinvolves only the free ions in the solution. Standard reference half-cells containKCl as an electrolyte, which normally oozes through a diaphragm to ensure thejunction with the analyte solution. To avoid perturbations when measuring K+

or Cl−, an electrolyte gel or a second non-interfering electrolyte (Figure 19.3) isemployed.

About 20 ISEs are used and classified according to the nature of the membrane.They serve either in direct ionometry, or as indicator electrodes for measurementsinvolving both titrimetry and complexometry performed with the aid of automatictitrators.

19.3.1 Single crystal and solid-state membrane electrodes

The fluoride electrode is the best known of the ISEs. Its sensitive membrane is amono-crystal of lanthanum trifluride doped with a europium salt, which allowsthe fluorine atoms to migrate within the cristalline network (Figure 19.3). TheOH− ion can cause interference with the F− ions at alkaline pH.

Crystalline powders agglomerated under pressure or with a suitable inertbinder (measurements of Cl−�Br−� I−�Pb2+�Ag+ and CN−) provide other mineralmembranes. The internal electrolyte can be eliminated (by dry contact). Howeverit is preferable to insert a polymer layer with a mixed-type conductivity to ensurethe passage of electrons from the ionic conductivity membrane towards the elec-tronic conductivity electrode (Figure 19.3).


"All solid"electrodes(without electrolyte)

Body of the electrode

Ag

AgCl AgClKCl

KNO3

Sample solution(contains fluoride ion)

LaF3

LaF3(monocrystal)

mV NaF (0.1 M)andNaCl (0.1 M)

AgF

Ag (thread)

Fluoride Chloride or sulfide

Ag2S/AgCl

Figure 19.3 Measurement set-up of ion-specific electrodes. Schematic of a measuring cell with aISE targeted for the fluoride ion using a double junction reference electrode. From the two sidesof the membrane two equilibria are produced, LaF3 →LaF+

2 +F−. To avoid osmosis of KCl intothe solution, the reference electrode is surrounded by a separate chamber which contains anauxiliary non-interfering electrolyte. KNO3 1M difficult to oxidize or to reduce, is often usedfor F−�Cl−� I−�CN−�S2− or Ag+. The measurement requires a high impedance millivoltmeter(type pH-meter). Right, two examples of simple to construct ‘coated wire electrodes’. A wireforms an ohmic contact with the membrane (ISE for fluorine with a LaF3 crystal and ISE forchloride with frit).

19.3.2 Liquid membrane electrode

The separation between the internal and external solutions of the specific electrodeis achieved using a porous and hydrophobic disc (of 3 mm diameter). This discis saturated with an organic solvent that is immiscible with water on either sideand contains also an ion-carrier called an ionophore (Figure 19.4). Hence, themembrane behaves as a lipophile immobilized liquid. The counter ion is a molecule

"Liquid membrane electrode"

Glass or polymer body

Ag/AgCl electrodecontaining an aqueous electrolyte of type MCl2(conc. Ref.)

Organic electrolyte

Porous membrane

Gas sensitive electrode

Reference electrode

Glass electrode

Internal solution

Polymer membrane(permeable to gasbut not to water)

Figure 19.4 Liquid membrane electrode and gas diffusion electrode. The ionophore is able tocomplex ions reversibly and to transfer them through the membrane. The gas diffusion electrodeis constructed in part from a pH electrode, which is plunged into an internal solution.

19.3 OTHER ION SELECTIVE ELECTRODES 459

OO O

O

O O

O

O

O

O

O

OO

O

O

OO

O O–Me

Me

Me

Me

P

Figure 19.5 Organic compounds used as ionophores. From left to right, three commercialchelating ionophores: ETH 129 and the ‘dioctyl’ phosphate, selective for Ca2+ ions and right,the K2 ionophore which is selective for the ion K+. Crown ethers of particular sub-structureare frequently used. Some are charged (liquid exchangers), other are neutral.

soluble in the organic phase. The primary interaction between the ion in waterand the lipophilic membrane is an extraction process.

For example, to measure calcium ions, an aliphatic diester of phosphonic acid�RO�2P�O�O− (Figure 19.5) can be used. On each side of the wall a concentrationequilibrium is established:

��RO�2P�O�O2Ca � 2�RO�2P�O�O− + Ca2+

solvent solvent aqueous phase

A measurable PD will appear if the concentrations of the calcium ions are differenton the two sides of the membrane.

19.3.3 Polymeric membrane electrodes

Many commercial selective electrodes include a membrane made of a plasticizedpolyvinylchloride (PVC) or polysiloxane film in which are disseminated variousion-carriers, ionic or neutral (Figure 19.5). Around 40 chelate molecules are usedfor around 10 common ions. Electrodes for CLO−

4 �BF−4 �NH−

4 �Ca2+ are of thistype.

19.3.4 Gas-sensing electrodes

Combined electrodes have been developed to measure dissolved gases such ascarbon dioxide �CO2�, ammonia �NH3� and sulfur dioxide �SO2�. These chemicalsensors contain an internal solution that is isolated from the sample solutionby an hydrophobic membrane which is permeable to dissolved gas molecules


(Figure 19.4). For the three gases given above, the selective electrodes includea glass electrode in contact with a bicarbonate solution of low concentration(0.01 M). The bicarbonate solution is separated from the sample solution by apolymer membrane that allows diffusion of the gas analyte towards the innerelectrode compartment.

This diffusion in the bicarbonate brings about a change in pH in the proximityof the membrane. For other gases, such as hydrogen cyanide (HCN), fluorhydricacid (HF) or hydrogensulfide �H2S�, the signal is generated by the modificationof the concentration of anions close to the internal wall of the membrane.

� The selectivity of an electrode is one of the most important characteristics. Amongdifferent methods that can be found in the literature the selectivity coefficient of aninterfering ion may be defined by Kspecific ion/interfering ion.

For example, KBr/Cl = 2.5 × 10-3 indicates that the selectivity of the electrode for

the bromide ion will be 1/2.5 × 10-3, that is 400 times greater than for the chloride ion.One other important factor is the response time, defined as the time between the

instant at which the selective electrode is dipped in the sample solution and the firstinstant at which the potential has reached 90 per cent of the final value.

19.4 Slope and calculations

Several methods leading to the determination of the sample concentration Ci ofan ionic species i exist. In the presence of a TISAB solution (see section 19.1), thatcan fix the pH, these methods are based on application of relation 19.3.

For a monovalent ion at 298 K, the slope factor S, that represents the term 2.303RT/F is equal to 0.0591 V (the theoretical slope). This is also the value of thegradient factor per pH unit for a glass electrode.

Ecell = E′′ + 0�0591

zlog Ci (19.4)

In practice the calibration curve Ecell = f �Ci� using a set of standard solutions,leads to the real slope (i.e. the experimental value of the slope factor), which is anindicator of the performance of the electrode system used.

Table 19.1 Values of the ideal slopes at 298 K for a few ions

Valence Ion Slope S (mV/decade)

−2 S− −29�58−1 Cl−�F− −59�16+1 Na+�K+ +59�16+2 Mg2+�Ca2+ +29�58

19.4 SLOPE AND CALCULATIONS 461

19.4.1 Direct ionometry

A series of standard solutions is prepared by successive dilutions of a stock solution.To each each solution, an excess but constant volume of the recommended ionicbuffer (ISAB or TISAB) is added. Sample solutions are prepared in the same way.Next, for each of the standards, the PD across the electrodes is measured and asemi-logarithmic curve E = f �Ci� is plotted (Figure 19.6). Finally, from this curveand the measured PD values for each of the sample solutions, obtained in thesame manner, the concentration of the species i is obtained. The precision ofmeasurements can be deduced from equation 19.5:

dE = RT

zF· dCi

Ci

that isCi

Ci

= E · zF

RT(19.5)

19.4.2 Standard addition method

The following technique may be useful to eliminate the effects of the matrix. Itrequires only one standard solution and two measurements of potential. However,the volumes must be known with a great precision. First, the PD E1 is measured

250

200

150

100

50

0

mV

59 mVTheoreticalslope

Molar concentration of chloride ion10–5 10–4 10–3 10–2 10–1

Figure 19.6 Typical calibration curve of an ISE by direct potentiometry. The calibration curveof the specific electrode for the chloride ion has almost an ideal slope value. The range oflinear response for the different ISE extends over 4 to 6 orders of magnitude depending onthe ion. Expression 19.5 leads to the estimation that an uncertainty of 0.2 mV on E leads toan inexactness of 0.8 per cent in the concentration (for a monovalent ion). Here, the TISABconsists of NaCl 1 M for adjusting the ionic force, a complexing agent for metals and a buffermixture of acetic acid/sodium acetate.


while the two electrodes (ESI and ERE) are immersed in a known volume VX ofthe sample solution of concentration CX in analyte. After adding to the abovesolution a small volume VR of a reference solution of concentration CR in analyte,the measurement of E is redone (new value E2).

The calculation, starting from expression 19.4, leads to a new expressiongiving CX:

CX = CR

VR

VR + VX

· 1(10E/S − VX

VR + VX

) (19.6)

where S represents the actual slope for the electrode used �0�0591/z at 298 K)and E = E2 − E1, the potential difference between the two measurementsE1 and E2.

� Instead of introducing the reference solution, a volume VX of the sample solutionat concentration CX can be added to a volume VR of the reference solution atconcentration CR. This alternative is preferable when sample solutions are relativelyconcentrated. Using E as above, it follows that:

CX = CRVX + VR

VX·(

10E/S − VR

VX + VR

)(19.7)

19.4.3 Potentiometric titration

Selective electrodes have a very variable specificity and a limited scope. However,precision can be increased when they are used as indicating electrodes in poten-tiometric measurements.

The concentration of ions present in solution and the ionic strength varyslightly during the measurement, relative to the concentration of the ion to bemeasured. This property can be taken into account when two ionic species undergoa stoichiometric reaction. In such cases, the end point in the measurement ischaracterized by either the complete disappearance of one of the species, or by theappearance of an excess of one of the species. The appearance or the disappearanceof a secondary species can also be useful to find the end point.

For example, to calculate the concentration of aluminium in solution, an ionfor which no selective electrode exists, this analyte is transformed into insolublealuminium fluoride AlF3 by adding sodium fluoride. The end point of this reactionis determined by the presence of an excess of sodium fluoride ions in solution,easily detected by a fluoride selective electrode.

A great number of commercially available automatic titrators perform similardeterminations.

PROBLEMS 463

� The lambda sensor, which is found in all motor cars with catalytic converters, isan oxygen probe based on the principle of selective electrodes. This sensor, whichlooks like a spark plug, has a zirconium oxide �ZrO2� membrane that behaves asa solid electrolyte. The external wall is in contact with the exhaust fumes while theinternal wall (the reference) is in contact with air. Between these two walls a PDappears, collected by two electrodes, which is indicative of the difference in oxygenconcentrations.

19.5 Applications

Potentiometric measurements are often used in routine analyses because they aresimple to achieve and the detection limit of the electrodes are on the order of10−5–10−6 M. However, the observed detection limit is governed by the presenceof interfering ions or impurities.

Some routine applications of the method are:

• in agriculture, the analysis of nitrates in soil samples

• in foodstuffs, the analysis of ions such as NO−3 �F−�Br−�Ca2+, etc. in drinks,

milk, meat, or fruit juices

• in industry, the analyses of chlorides in paper paste, cyanides in electrolysisbaths, chlorides and fluorides in galvanic processes

• in clinical chemistry, the analysis of certain ions in serum and other biologicalfluids.

Problems

19.1 Consider an aqueous solution of ammonia, 9 × 10−3 M, to which isintroduced a quantity of ammonium chloride in order to attain a pH of 9.At this precise moment, what is the concentration of the salt?

�KB NH3 = 1�8 × 10−5�

19.2 Explain how the electrode’s glass membrane registers the pH of an aqueoussolution.

19.3 What is the degree of dissociation and the pH of an aqueous solution of0.85 M ethanoic acid? (KACH3CO2H = 1�8 × 10−5 at 20 �C.)


19.4 30 mL of an 10−3 M aqueous solution of an Fe3+ salt is mixed with 20 mL ofa 10−3 M solution of a salt of Ti3+. What will be the molar concentration ofthese salts following reaction in this modified solution? (Ti3+/Ti4+ = 0�2Vvs. SHE; Fe2+/Fe3+ = 0�77 V vs. SHE and SCE/SHE = +0�25V).

19.5 Knowing that the standard potential of an electrode Cd/Cd2+ vs. SHE, hasthe value 0.404 V, what happens to this potential if the electrode is plungedinto an aqueous solution of 0�01MCdSO4?

19.6 Find the expression 19.6 of Section 19.4.2 used in the standard additionmethod.

20Voltammetric and coulometricmethods

In contrast to potentiometry that operates under zero current conditions, otherelectroanalytical methods impose an external source of electricity to the samplesolution, to induce an electrochemical reaction that would not otherwise sponta-neously occur. It is thus possible to measure all sorts of ions or organic compoundsthat can either be reduced or oxidized electrochemically.

Polarography, the best known of all voltammetric methods, is still nowadaysa competitive technique for the measurement of trace elements, ions or organiccompounds, although is implementation is rather delicate.

Coulometry is the name given to a group of other techniques that determinean analyte by measuring the amount of electricity consumed in a redox reaction.There are two categories referred as potentiostatic coulometry and amperostaticcoulometry. The development of amperometric sensors, of which some are specificfor chromatographic detection, open new areas of application for this battery oftechniques. Combining coulometry with the well known Karl Fischer titrationprovides a reliable technique for the determination of low concentrations of water.

This chapter is an overview of the most important methods in this domain.

20.1 General principles

Voltammetric methods consist of applying a variable potential difference betweena reference electrode (e.g. Ag/AgCl) and an indicator electrode, called the workingelectrode. On its surface a reaction of type Ox + ne → Red (or its reverse) isinduced. When the potential at the working electrode reaches a value such that aspecies (the depolarizer) present in the solution being studied, is either oxidizedor reduced, the current through the circuit outside to the cell increases sharply.In practice, in order that no current passes through the reference electrode, athird electrode called the auxiliary electrode (or counter electrode), made of an inertmetal or carbon employed along with a support electrolyte is used to make themedium electrically conductive (Figure 20.1). The microelectrolysis that occurs


466 CHAPTER 20 – VOLTAMMETRIC AND COULOMETRIC METHODS

Potential relative to the reference Ag/AgCl

Pt

Au

VC

Electrolyte: H2SO4 1M

Hg

+ 1.5 + 1 + 0.5 0 – 0.5 – 1 – 1.5V

Currentmeasurement

(d) (e)

Mercuryreservoir

(c)(b)(a)Conductor

Aux.

Capillary

Work. Work.Ref. Ref.

Mercury droplet

++ ––

ex. SCE ex. Pt

mV

mV

Potentiostat

Ref. Working Aux. Output

Input

µAµA

Figure 20.1 Schematics showing 2- and 3-electrode cells. (a) Circuit diagram with two electrodesthat is not used in practice as this assembly has the major inconvenience that the current passesthrough the reference electrode which should be avoided because its potential will be modified;(b) DC set-up in which no current passes through the reference electrode (a consequence ofits high impedance); (c) A model indicator electrode (hanging-drop mercury electrode). Manymetals can be reduced at the surface of the mercury before H+ is reduced in its turn (productionof hydrogen gas); (d) Representation of a measuring cell controlled by a potentiostat; (e) Rangesof use for the four principal working electrodes in sulfuric acid 1 M as support electrolyte (VCstands for vitreous carbon). The mercury electrode can be used over a wide cathodic rangewith electrolytes such as KCl or NaOH �−2V�. Although overlaps are observed with differentelectrodes, their sensitivities can be quite different for a given species.

over a short period during measurements does not notably alter the concentrationof analytes in the sample solution.

Briefly, a voltage scan over a range where oxidation or reduction of the analyteis expected, gives a voltammogram that is an S shaped curve displaying currentvs. voltage, I = f �E�. This plot permits the identification and measurement of theconcentrations of each species of interest.

The most widely used working electrodes are made of vitreous carbon, platinum,gold or mercury (Figure 20.1). They are flexible in the sense that they can beused between two potential values that depend on the support electrolyte, the pHand the reference electrode. These limits, for example, for a platinum electrodeare +0�65V relative to the standard calomel reference electrode (SCE) (to avoidoxidation of water: H2O → 1/2O2 + 2H+ + 2e−� and −0�45V (to avoid reductionof water: H2O + 2e− → H2 + 2OH−).

20.3 DIRECT CURRENT POLAROGRAPHY (DCP) 467

� An electroanalytical voltammetric experiment necessitates a potentiostat. Whenused in the usual three electrode mode, this device controls the voltage across theworking electrode/auxiliary electrode pair. The voltage is adjusted to maintain thepotential difference between the working and reference electrodes. So the workingelectrode potential is maintained, even if a current flows. The cell output provides ameasure of the current that flows between the working and auxiliary electrodes. Whencoupled with a suitable signal generator, it can be used to a variety of voltammetricmethods.

20.2 The dropping-mercury electrode

The most original working electrode contains an active mercury micro-dropper.The voltammetric technique making use of this electrode is called polarography,invented by Heyrovsky in the 1920s.

This electrode is constituted of a glass tube, maintained in a vertical position,of which the central passageway �10–70�m in diameter), allows the transfer ofmercury between a reservoir and the capillary tip, where very small droplets areformed. This dropping-mercury electrode is immersed in an unstirred solutioncontaining the target analyte mixed with a support electrolyte. The surface ofthe droplet of mercury increases until it falls (around 4–5 s). The fall is mostoften provoked by a device producing a small impact on the electrode. Instanta-neously, a new droplet, identical to the previous one, is formed presenting a freshuncontaminated surface.

This electrode, rather out of the ordinary, has some inconveniences. Themercury must be very pure (six-time distilled and conserved under nitrogen). Itsvapours are poisonous, and after use it must be at least recovered and re-cycled.

20.3 Direct current polarography (DCP)

In the basic experiment – now rarely used – a linear changing time-dependantpotential is applied to the mercury droplet, in the order of v = 1–2 mV/s from theinitial potential Ei selected. So, it can be written:

Eworking − Eref = Ei ± vt (20.1)

The sign ± of the equation 20.1 signifies that the sweeping can be performedeither on the anodic �V > 0� or cathodic �V < 0� side. The resulting currentvoltage curve I = f �E� is a polarogram, which can show one or several waves(Figure 20.2). The height of each step, corresponds to the limiting diffusion currentiD (cf. section 20.4) and is a function of the concentration of the depolarizer(the analyte, which is reduced on contact with mercury), which thus allows its


–0.2 –0.2–0.3 –0.4 –0.5V –0.5V

Inte

nsity

0.2 µA

Voltage

Residual current

Limiting current

Diffusion currentiD

/2

E1/2

µAµA

Figure 20.2 A polarographic wave. Polarogram of a solution containing 10 ppm of Pb2+ inKNO3 0.1 M, obtained with a dropping-mercury electrode. The median position of the wave(about −0�35V ) is characteristic of lead while the height of the step, of its concentration. Fora better presentation of the graph the oscillations have been damped. Right, a graph shows themeasure of iD. The residual current is due in part to impurities in the support electrolyte andto traces of oxygen.

quantitative determination. Each analyte is characterized by a half-wave potential,determined at the mid-height iD/2, of its wave. As a result, several species presentin a solution can be studied during the same analysis, on condition that theirhalf-wave potentials are sufficiently different. The polarogram shows also a saw-toothed fine structure, which is produced from the continuous renewal of themercury droplets.

The mercury is quickly limited at positive potentials (+0�25V with respect tothe SCE) beyond which it is oxidized in its turn. Instead, for negative potentials itis usable up to −1�8 or −2�3V depending upon whether the supporting electrolyteis acid or alkaline. This range offers many possibilities in analysis, particularly forthe determination of heavy metals.

The elimination of all traces of dissolved oxygen in the solution by nitrogenbubbling is essential otherwise the polarogram would be inexploitable by effect ofthe reduction of oxygen in water according to the two steps detailed in Figure 20.6.

An advantage of voltammetry over AAS is the ability to distinguish an elementin different valence states. For example, iron Fe2+ can be quantified apart fromFe3+ (cf. Figure 20.4). Some organic molecules are equally electroactive and canbe analysed by this method.

20.4 Diffusion current

The particular features appearance of the polarographic wave can be explained asfollows. Suppose that a sample solution contains a very much diluted lead salt�Pb2+� in a support electrolyte whose concentration is much greater than that

20.4 DIFFUSION CURRENT 469

of the Pb2+. To the working electrode a negative linearly increasing voltage isapplied from a starting value lower than required to reduce Pb2+. At −0�35V (vs.Ag/AgCl), the Pb2+ ions are reduced upon contact with the mercury droplet. K+

ions, non-reduced at this potential, will form a shield around the drop preventingthe normal migration of the other Pb2+ ions in the solution. However, under theeffect of a concentration gradient, these Pb2+ ions will reach the surface of theelectrode – where they will be reduced – only by diffusion across the layer of K+

ions. This phenomenon is the basis of the diffusion current. The average limitingvalue of the diffusion current iD, is essentially due to the ion flux of the analyteconsidered at the instant that precedes the falling of the drop. It depends uponseveral parameters one of which is the capillary constant, �m2/3 · t1/6�

iD = 607 · n · D1/2 · m2/3 · t1/6 · C (20.2)

iD is expressed in �A with the following units: D, diffusion coefficient of theanalyte ion �cm2/s��m, mass flow of mercury (mg/s); t, lifetime of the droplet(s); C, concentration of analyte �mmol/cm3�; n the number of electrons trans-ferred during the electrolysis of the ion. The coefficient 607 is established for25 �C.

This expression – known as the Ilkovic equation – which takes into accountseveral factors, is replaced by the simplified formula 20.3 where K includesparameters related to the method and instrument used. K is a constant for a givenanalysis.

iD = KC (20.3)

Experimentally the current passing through the droplet is the result of severaleffects, amongst which are:

• The capacitive current which makes droplet/electrolyte interface analogous toa capacitor by fixation of electrons that face the ions of support electrolyte(e.g. K+). This capacitive current diminishes very quickly with time becauseit depends upon the variation of the droplet surface area, which decreases asthe droplet expands.

• The diffusion current (Faraday-type current) which decreases as t1/2 if thesurface of the drop does not vary, but increases taking account of the growingpotential applied to the drop and its growing surface. This expansion ofthe droplet’s surface more than compensates for the depletion of electroac-tive substance in close proximity to the electrode. The graph displaying theintensity has at last the appearance shown on Figure 20.3.

� The tast polarography consists of measuring the current only for a very shortperiod, late in the lifetime of the drop. This current sampling avoids the saw-toothedspikes on the current curve. Yet it leads to a reduction in sensitivity since the diffusioncurrent decreases as the analyte flux moves from the bulk of the solution to thesurface of the droplet (Figure 20.3).


N2ID

Current Instant of drop fall

Time

2 – 4s 2 – 4s

Duration of sampling for the "tast" technique

mV µA

1 2 3

1 - Ref. electrode2 - Working electrode3 - Auxiliary electrode

average

Figure 20.3 Polarographic cell and diffusion current. The solution must be free from dissolvedoxygen which otherwise causes an interfering double wave (see Figure 20.6). On the right,graph of the diffusion current, growing over time for each drop of mercury in a static solution(unstirred solution). Direct polarography is a slow method of analysis. The recording of avoltamogram requires at least one hundred droplets. A calculation of iD max is possible withthe Ilkovic equation if the coefficient 607 is replaced by 706 in equation 20.2.

20.5 Pulsed polarography

To improve the sensitivity and to be able to distinguish the analytes for whichthe half-wave potentials differ by only a few tens of mV, the mercury drop is nolonger submitted to a gradually increasing voltage but rather to a pulsed voltage.Two major modes of operation coexist.

20.5.1 Normal pulsed polarography (NPP)

To eliminate the jagged appearance of the classic polarogram the standard voltageramp described earlier is replaced by a series of brief pulses (between 50 to100 ms), of increasing potential. The pulses are delivered at the same frequencyas the mercury drop renewal (between 2 and 4 s). Each pulse begins at the samevoltage low enough to avoid the reduction reaction of the analyte (Figure 20.4).Electrolysis is thus blocked between each pulse. Current measurements are madejust prior to the fall of the droplet. At this instant the Faraday diffusion currentis stabilized while the capacitive current has become negligible. The sensitivity ofthe basic method here gains 2–3 orders of magnitude.

20.5.2 Differential pulsed polarography (DPP)

A pulse of 50 mV is applied during 50 ms to the working electrode for eachsuccessive droplet of mercury. The first measurement is made just before thepulse and the second just before the droplet falls (Figure 20.4). In this way, the

20.5 PULSED POLAROGRAPHY 471

NPP

DPP

mV

vs.

Ag/

AgC

l

50 mV

0

1

2

0 –0,5 –1

–0,3V, Fe++

–0,9V, Fe+++

Sig

nal

a

a

b

Potential vs. SCE

Blank

L(+) Ascorbic acid dehydro-ascorbic acid

–0.1 0–0.15 +0.1 +0.3 V

1

2

Supporting electrolyte :Acetate/acetic acid buffer

Fruit juice (diluted with water)

Fruit juice with added ascorbic acid

Pulse amplitude 25 mVDrop interval 1 sSweeping speed 2 mV/s

1

2

2–4s

0

Time50–100 ms

mV

vs.

Ag/

AgC

l

2 – 4s

0

Time

50–100 ms

Potential mVvs Ag/AgCl

0

1

2

Cur

rent

(µA

)C

urre

nt (

µA)

Fe++/Fe+++

0.1 M pyrophosphate buffer, pH 9

Drop evolution

O

O

OH

OH

HOH2C

HOH

O

O

OO

HOH2C

HOH

+2H+–2e–

Cr6+, Electrolyte 1M NaOH

–0.7 –0.85 –1

Figure 20.4 Pulsed polarography. NPP and DPP techniques. The diagram shows at whichinstants the measurements are made (see the arrows a and b). Examples of measurements. Themeasurement of ascorbic acid (vitamin C) in a fruit juice (see conditions) corresponds to anoxidation on the working electrode.

two currents are measured on the same drop but with a difference of 50 mVvoltage. The graph of the difference of these currents, as a function of thevoltage, exhibits a peak for each analyte, whose height is proportional to itsconcentration.


Hydrocarbons

Phenols

Amines

Ethers

Ketones

Olefins

Electroactive region (vs. SCE)of several organic compounds

+2 +1 0 volts –1 –2

Outlet

Outlet

Inlet

Inlet

Aux.Work.Ref.

Ref. Aux. Work.

2.

1.

(b)(a)

2 cm

1 mm

Auxiliaryelectrode

Referenceelectrode

Capillary tipWorkingelectrode

Figure 20.5 Amperometric detection in HPLC and HPCE. (a) Two models of detector cells.The porous graphite working electrode have a large surface and operates under coulometricconditions. The flow of the mobile phase at the working electrode ensures renewal of theelectroactive species; (b) Detail of the end of a capillary in HPCE. The working electrode, placedon the cathodic side of the apparatus, is bathed by ions exiting the capillary. Apart from phenols,aromatic amines and thiols, few analytically important molecules are electroactive.

20.6 Amperometric detection in HPLC and HPCE

Voltammetry has been applied to a highly sensitive mode of detection for elec-troactive compounds in liquid chromatography (providing the mobile phase isconducting) and capillary electrophoresis. The voltammetric cell has to be minia-turized in order not to dilute the analytes after separation. The metal or carbonworking microelectrode has a defined voltage with respect to the reference elec-trode (depending on the substance to be detected) and the detection cell is sweptby the mobile phase as it leaves the column (Figure 20.5).

20.7 Amperometric sensors

Voltammetric measurements are not simply restricted to analytical laboratories.The applications of these methods are more numerous than is at first obvious.A large number of analytical instruments, whether portable or not, intended tomake precise measurements of substrates present in gas mixtures, vapours orsolutions are equipped with electrochemical sensors. These devices operate on theprinciple of the 2- or 3- electrode cell enclosed in the sensor housing.

20.7 AMPEROMETRIC SENSORS 473

20.7.1 Clark oxygen probe

The electrochemical reduction of oxygen in contact with an electrode providesthe basis for several models of sensors, which differ only by the reactions used.The best known of these is without doubt Clark’s oxygen sensor, which containsa silver anode and a platinum cathode (working electrode), which are both incontact with a KCl solution (Figure 20.6). This electrolyte is separated from thesample by a Teflon membrane that is porous to oxygen but impermeable to theelectrolyte. After crossing this membrane the gas comes into contact with thecathode, about 10�m distant from the inner face of the membrane. A potentialdifference PD of around 1.5 V is applied between the two electrodes, the cathodebeing brought to a potential sufficiently negative to reduce all of the oxygen(reactions 1 and 2). The current in the circuit is proportional to the quantity of gasmigrating across the membrane and consequently to its concentration in solution(Faraday’s law).

The manufacture of electrochemical sensors has evolved considerably and theirproduction has diversified. The three electrodes of the sensor shown in theexample of Figure 20.7 result from a manufacturing technique characteristic tomicroelectronic circuits. Completed by a membrane and an electrolyte, this sensoris used to measure chloride dissolved in water. Based upon the oxidation of theClO− (hypochloric acid) ion its detection limit is 1 ppb.

+–

Buffer solutionwith KCl 0.1 M

Teflon membrane

Sample solution

Summary:

Sensor body

Insulating material

PD 1.5 V

Annular Ag auxiliaryelectrode (anode)

Pt working electrode(cathode)

the two polarographic waves of oxygen

Cur

rent

2

1

–0.35 –1.25 VApplied V vs. NHE

= O2 + 4H+ + 4e–

O2 + 2H+ + 2e–

4Ag + 4Cl– 4AgCl + 4e–

+ H2O2 + 2H+ + 2e–

H2O2

2H2O

2H2Oat the anode:

at the cathode:

at–0.35 V

at–1.25 V

µA

Figure 20.6 A Clark sensor for oxygen determination. Cell housing two concentric electrodes.The Teflon membrane, permeable to oxygen, must be very close to the cathode so that thedouble diffusion process through the membrane and subsequently the liquid film will lead to astable signal after a few seconds.


1 - Silicon support2 - Silicon nitride (insulator)3 - Auxiliary electrode (platinum)4 - Working electrode (platinum)5 - Reference electrode (Ag/AgCl)6 - Polymer (polysiloxane)7 - Specific membrane8 - Connections

Overall dimensions: 6 × 4 mm.

2

3

2

3

34

4

5

5

6

6

7

7

8

8

a

transection ab

1

45

b

Figure 20.7 Sensor issued from a microlithography technique. Sensor for measuring chloride inaqueous media. Diagram representing a document from Microsens (CH). Sensor MAES-2402.In this diagram, the thicknesses of the circuits are not to scale. This assembly is not completesince it lacks certain elements of the sensor (electrolyte, connections).

20.7.2 Other amperometric gas sensors (AGS)

Many toxic contaminants �SO2�NH3�PH3�CO � � �� can be measured by means ofsubstance-specific electrochemical sensors designed from the classic system of twoor three electrodes already discussed. The corresponding instruments are mostlyused for a variety of hazardous and confined space applications (Figure 20.8).Being sensitive and having a rapid response time, when the working electrodeis covered by a catalyst, they can be used over a wide range of concentrations(4 orders of magnitude). In contrast they function over a restricted temperaturerange �−10/+ 40 �C�, requiring re-standardizing. Their lifetime is normally of afew years, depending of stocking conditions.

When the AGS is exposed to a gaseous mixture, the electroactive species forwhich it was designed reaches the working electrode where a redox reactionoccurs. For example, an oxidation reaction results in flow of electrons fromthe working electrode to the auxiliary electrode through the external circuit.This flow of electrons constitutes an electric current, which is proportionalto the gas concentration. The potentiostat can modify the electrode poten-tials, allowing different analytes to be measured on condition that the detectoris changed.

The H2S AGS described below corresponds to a typical arrangement(Figure 20.9). The main parts of this sensor consist of three porous noble metal


Figure 20.8 Amperometric gas sensors. Assortment of sensors from ATMI Sensoric Div. (Ger.).Model GasAlertMax3-DL from BW Technologies (Can); a view shows a model including fourspecific detectors. Flowing across a specific diffusion barrier, the gases are oxidized (CO, H2S,NO, H2, HCN) or reduced �Cl2�NO2� in the presence of an electrolyte. This electrolyte isprogressively contaminated with by-products, and like non-rechargeable batteries, their life islimited.

electrodes and an acidic aqueous electrolyte, housed within a plastic enclo-sure. The reference electrode is totally immersed in the electrolyte. It remainsat the same potential, and is used to regulate the potential of the workingelectrode even if a current is generated during operation. Gas enters the cellvia a capillary followed by a charcoal filter that removes unwanted inter-fering gases. Any hydrogen sulfide present undergoes the following oxidationreaction:

H2S + 3H2O → SO3 + 8H+ + 8e−

The SO3 generated either escapes from the capillary or dissolves in electrolytesolution to form sulfuric acid. Hydrogen ions migrate within the cell, and finallygive rise to water using oxygen from the surrounding atmosphere. The electronsconsumed in this reaction are supplied by the external circuit. By connecting theworking and the auxiliary electrodes, the current (a few nA) generated betweenthem is measured as directly proportional to the concentration of H2S in the air.This very weak current gives explanation of the rather long life of many AGSdevices: 10 nA for 1 year corresponds to only 0�3C, a insignificant quantity ofelectricity for an important electrolysis.

Two other examples on the figure relate the reactions which occur in AGSfor carbon monoxide (CO) and for oxygen �O2�. The electrolytes are, for CO,a strong mineral acid such as sulfuric acid, while for O2 it consists in a weaklyalkaline solution with potassium acetate. These liquid electrolytes are immobilizedby absorbent materials.


Auxiliary electrode

Sample gasSample gas

Sample gas

Working electrode(CO or O2 sensing electrode)

Carbon monoxyde cell

Hydrogen sulphide (H2S) cell

Oxygen cell

Connectors pins

Oxygen

Separator

Acidelectrolyte

O2 + 2H2O + 4e–

2PbO4OH– + 2Pb

Capillary hole

Work.

Anode

Ref. Ref.Aux. Aux.

Glass fiber

Outer casing

H2S SO3

O2

H+

H2OH2O

Electrolyte

Potentiostat

OutputR

Some chemicals concernedwith an H2S AGS

Charcoal filter

e–

e–

(with eventually a placement pin)

Acidelectrolyte

External moisture barrierDiffusion barrierwith diffusion capillary

Cathode

SO3 + H2OH2S + 2O2

H2O2H+ + 2e– + 1/2O2

CO + H2O CO2 + 2H+ + 2e– 4OH–

Lead (anode)+

Basic electrolyte

Figure 20.9 AGS, principles of operation. Cells for hydrogen sulfide, for carbon monoxide andfor oxygen. For hydrogen sulfide sensor, the reference electrode helps to extend the workingrange of the sensor and improves the linearity of response. The electrochemical reactionsconsume the species present in the cell. This can be the anode itself (cell for oxygen), theelectrolyte or even a reagent which should be present (oxygen is necessary for the cell detectingcarbon monoxide).

20.7.3 Biosensors employing amperometric detection

A biosensor contains a compound of biological origin (enzyme, antibody) includedin a device holding the electrodes in order to convert a biological signal (e.g.fixation of the antigen to the antibody) to an electric signal.

To make the biosensor specific for an analyte, a membrane is generally usedthat contains a recognition layer trapping the specific enzyme that catalyses the


transformation of the analyte. This could be a sandwich system in which theenzyme is immobilized between an external cellulose acetate membrane to preventthe passage of heavy molecules and an internal polycarbonate membrane thatallows passage of the transformed product to the electrode.

In this area, for insulin-dependent diabetes, there is a miniaturized device formeasurement of glucose in blood which uses to assure electron transport glucoseoxydase (GOX) and either oxygen or a mediator such as quinone or a conductingpolymer (Figure 20.10).

For this measurement successive generations of biosensors have adopted thesame principle; The mechanism of operation is as follows : glucose is oxidized togluconolactone, the key reaction, by the oxidized form of glucose oxidase (GOX)an enzyme produced by Aspergillus niger. This enzyme contains a flavin-basedprosthetic site, which serves as a provisional trap for electrons, by passing from itsoxidized form (flavin adenine dinucleotide, FAD) to its reduced form �FADH2�.Two protons and two electrons are transferred to the enzyme as it passes to itsreduced form. To return to its initial oxidized state FADH2 reacts with eitheroxygen with formation of a molecule of hydrogen peroxide (first generation),or with an oxidant (called a mediator, e.g. quinone), that is easy to mix withthe enzyme of known concentration (second generation). This second procedureimproves the measurement selectivity.

Ruced mediator Oxidised mediator

Glucose Gluconolactone

in contact with the Pt anode(+ 600 mV vs. Ag/AgCl)

Details of the active section

3 - Selective membrane2 - Immobilised enzyme and mediator1 - Measurement electrode

Ox. form GOX.(enzyme)

–2e–

+ 2e–

+ 2e–

–2e–

O2H2O2

CO

H

carbon1

+ + + + +

2

3

CO

O(C)

GOX-FADH2GOX-FAD

1st generation

2nd generation

Red. form

or

Glucose Proteins

on Pt electrode

Figure 20.10 Amperometric measurement of glucose. Left, reactions cycle in first and secondgeneration devices. Right, a sandwich-type biosensor involving glucose oxidase. O2, or a medi-ator, are necessary because they are small molecules that may reach the prosthetic group of theenzyme, liberating hydrogen peroxide that diffuses to the surface of the platinum electrode. Themediator could equally be a redox system based upon osmium immobilized in a polymer. Thereaction can be followed by monitoring oxygen consumption or H2O2 formation.


Protecting membrane

Insulating bodySolution

Reference electrode

Selective membrane

Source Enzyme layerDrain

–+

Grid

Channel layer

Source

isolator (SiO2)

Insulator (SiO2)

Drain

a n-FET

pnn

p-type Siliconn-type Silicon

Semiconductor

5 mm

Figure 20.11 A selective electrode based on the principle of the field effect transistor. By placingthe enzyme in contact with the electrode, it is possible to follow a specific reaction. The surfaceof silicon (sites of silanol functionality) is particularly sensitive to H+ ions.

The amperometric sensors utilize reactions occurring on contact with theworking electrode. This category of electrochemical sensor is large. Other formsof detection are met : a urease may be used to transform urea into ammo-nium ions which will be detected by a selective electrode for those ions, ora penicillinase which will destroy penicillin releasing H+ detected by a pHelectrode.

� A particular type of biosensor is based upon the principle of the field effecttransistor (FET) in which the semi-conducting layer is in contact with a membraneincorporating an enzyme adapted to transform a particular analyte (Figure 20.11).The chemical reaction in contact with the enzyme will modify the polarity of theinsulating layer. This in turn will modify the conduction between the source and thecollector (drain) of this transistor. The current between these two electrodes servesas the signal.

20.8 Stripping voltammetry (SV)

Two very sensitive methods, called anodic and cathodic stripping voltammetry(SV), are used to measure trace of metal. They are carried out in two stages:

• Preconcentration. A fraction of the target electroactive analyte is deposited, ina few minutes, on an electrode held at a constant potential and immersedin a stirred solution of the sample. This electrode can be a hanging mercury

20.8 STRIPPING VOLTAMMETRY (SV) 479

droplet (non-renewed) or a cylinder of vitreous carbon covered by a mercuryfilm or a rotating carbon disc with addition of a mercury salt in the solution.In all cases the surface of the electrode gives an amalgam M(Hg) with metallicanalytes Mn+.

• Re-dissolving. Following electro-deposition, mixing of the solution is stoppedand the potential difference is progressively reduced between the workingand reference electrodes. Due to reversibility of redox reactions, it appears anelectrochemical oxidation of the analyte which is redissolved. The elementsare identified by their oxidation potential.

The example given on Figure 20.12 corresponds to anodic voltammetric analysis.When combined with the technique of DPP (Section 20.5.2), stripping voltam-metry constitutes the most universally applied voltammetric method. Currentinstruments for which control of all the parameters is established, allow repro-ducible conditions and offer an alternative to spectroscopic methods such as atomicemission.

Potential in V(vs. Ag/AgCl)

Applied potential V vs. Ag/AgCl electrode. Time: 5 min.

Polarogram of a mixture of 4 metal ions1.5

1.0

0.5

Graphite electrode

Insulating body

Zn: – 1.08 VCd: – 0.66 VPb: – 0.49 VCu: – 0.08 V

–1.3 –1.1 –0.9 –0.7 –0.5 –0.3 –0.1 +0.1

Zn CdPb

Cu

0

Peak potentials

–1,2

–0,8

–0,4

00 5 10 min

µA

Figure 20.12 Stripping voltammetry. Linear voltage programming of the working electrode.Example of an electrode. Analysis of four metals present in a sample of sea water byDPP.


20.9 Potentiostatic coulometry and amperometriccoulometry

The methods described previously correspond to the partial electrolysis of theanalytes in contact with the working microelectrode. By contrast coulometricmethods are based upon stoichiometrical relationships (quantitative conversionof the analytes). The concentration of an analyte is calculated from the quantityof electricity, using the equation Q = it. Standardization or calibration curves arenot required. This is not therefore a comparative method.

Two types of coulometric methods co-exist:

• The potentiostatic coulometry, involves holding the electric potential (thevoltage) of the working electrode constant during the reaction. This avoidsparasitic reactions. The current decreases as fast as the analyte disappearsfrom the solution. A galvanostat (or amperostat) is used to compute thequantity of current used.

• The coulometric titration or amperostatic coulometry method in which thecurrent is maintained constant during the measurement by an amperostatuntil the signal which marks the end of the reaction with the analyte. This isthe most simple form of coulometric measurement.

Both techniques take place within an electrochemical cell. A coulometric titratorequipped with a working electrode of large surface area and an auxiliary electrodeseparated from the reaction compartment by a diaphragm. This protection of thesecond electrode provides a barrier between the species formed in contact withit and those formed at the working electrode thus avoiding an eventual reaction(see Figure 20.14).

Often, direct and total transformation of the analyte proves difficult because theproduct formed accumulates in contact with the electrode, causing a polarization.This problem is countered by addition of a precursor in large excess, which isemployed for the liberation of an intermediate reagent that will react with all theanalyte. In this way the compound being analysed does not participate directly inthe electron transfer procedure. This is the case in the coulometric adaptation ofthe Karl Fischer determination of water, described below.

� Thus, the measurement of Cl− ions will be possible from Ag+ ions generated fromthe surface of a silver electrode. The quantity of current used, in coulombs, leadsto a precise calculation of the quantity of analyte transformed on condition that thecurrent serves only for the formation of ions Ag+. Standard solutions are not requiredfor these measurements. The absolute quantity of ions formed is determined fromthe current consumed. The quantity of current Q(C) = i(A) · t(s) corresponds to asingle analyte.

20.10 COULOMETRIC TITRATION OF WATER BY THE KARL FISCHER REACTION 481

20.10 Coulometric titration of water by the Karl Fischerreaction

Many manufactured products, as well as solvents and raw materials are analyzedfor their water content (percent humidity). Of all the available methods, the KarlFischer titration is perhaps the most widely used, accounting more than 500 000determinations performed daily world-wide.

The Karl Fischer method is applied in a multitude of substances from finishedproducts (butter, cheese, dried milk sugar, etc.) to solvents and other industrialproducts (paper, gas, petroleum, plastic films, etc.). Solids and not soluble samplesmust, prior to the measurement, either be ground into powders, extracted withanhydrous solvents, eliminated as azeotropes or heated to evaporate the water inspecial accessories. The only difficult cases are encountered with strongly acidic orbasic media since they denature reactants as well as ketones and aldehydes whichperturb the titration through formation of acetals (special reagents must be usedfor these instances).

This method of titration may be sub-divided into two main techniques: volu-metric titration making use of a titrator (a potentiograph) with end point detec-tion, and coulometric titration making use of a coulometer, more sensitive formeasurement of very low levels of water (concentrations in the order or below1 mg/L).

20.10.1 Reactions involved

In the presence of water, iodine reacts with sulfur dioxide through a redox reactionthat is specific to these three compounds:

2I + SO2 + 2H2O → H2SO4 + 2HI

This quantitative reaction can be used to determine water and can be achieved if,for example, a base is added to neutralize the acids formed – for this reason, KarlFischer used pyridine.

Since iodine is a solid and sulfur dioxide is a gas, an auxiliary polar solvent isused which serves as both a diluent and as a reaction medium. Generally, methanolis used, though in rare cases the methylmonoether glycol, or diethylene glycol,are also used. Under these conditions sulfur dioxide is not simply dissolved in thesolvent but interacts with it, leading with methanol to methylhydrogenosulfite.This latter becomes the species that reacts with the iodine in the presence of water.

CH3OSO2H + 2I + H2O → CH3OSO3H + 2HI

In contrast to the first reaction, in the presence of methanol, a single molecule ofwater reacts to convert two atoms of iodine. Methylhydrogenosulfite is oxidized to


hydrogenosulfate, converted in the presence of a base of type RN into an ammo-nium salt. The Karl Fischer reaction can therefore be reformulated as follows:

H2O + 2I + RNH+CH3OSO−2 + 2RN → 2RNH+I− + RNH+CH3OSO−

3

With pyridine as a base, a pyridinium salt C5H5NH+�CH3OSO3�− is formed.

This base, with its highly disagreeable odour, is now replaced by imidazole ordiethanolamine, both odourless and leading to more stable commercial reagents.

Because atmospheric humidity must be avoided, the reaction cell is isolatedfrom the atmosphere by drying tubes. Moreover, since the diluting solvent israrely anhydrous, owing to its hygroscopic nature, its water content must bedetermined prior to the measurement. The end point of the reaction is detectedby the variation of an alternate current intensity that passes between two smallpolarized platinum electrodes inserted in the reaction medium (Figure 20.13).

When using a titrator, the Karl Fischer reagent (KF reagent) is a mixture ofsulfur dioxide, iodine and the base, characterized by the number of mg of waterthat can be neutralized by 1 mL of this reagent. This is referred to as the equivalentmass concentration of water, or the Titer T of the reagent.

In the classical method, two steps are involved in the analysis. First, the waterequivalence of the KF reagent (Titer T ) is determined. Then, the water containedin the sample is measured. As for many volumetric measurements it is possible tofollow either a method of direct titration or back titration. In the direct titrationthe end point is reached by gradual addition of the KF reagent. By back titration,an excess of this reagent is introduced, then the excess is measured using anon-anhydrous solvent for which the water equivalence has been determined bypre-titration and which has subsequently been placed in the burette.

Detector

Sample

Magnetic stirring bar

(Nitrogen)

SolventK. Fischer reagent

Figure 20.13 Measurement of water by the Karl Fischer volumetric technique. The titration cellcontains volumetric burettes (which may be automated) and two small platinum electrodes. Aslong as no iodide is present in solution the electrodes remain polarized and only a weak currentcirculates between them. Once the equivalence point is reached, an excess of iodine will causethe depolarization of the electrodes and a significant current is registered.

20.10 COULOMETRIC TITRATION OF WATER BY THE KARL FISCHER REACTION 483

� Water standards generally consist of a precision-weighed mass of a solid hydrateof known composition: oxalic acid at 2H2O (28.57 per cent in water), or tartrate ofsodium at 2H2O (15.66 per cent in water).

20.10.2 Coulometric adaptation of the Karl Fischer reaction

To obtain results of acceptable precision from the volumetric technique, at least10 mg of water must be found in the sample, given the magnitude of the equivalentwater Titer T of the commercially available KF reagent (several mg/mL). Whenthe amount of water is lower (as low as 10�g of water) the coulometric versionoffers many advantages.

The coulometric technique is based on the same chemistry but its fundamentaldifference is the way by which the iodine is introduced into the titration cell(Figure 20.14).

The iodine necessary for reaction is generated from a precursor by applyingelectrical pulses to the electrode. Thus, the modified KF reagent contains an iodide(the precursor) which is oxidized to iodine in contact with the working anode�2I− → 2I + 2e−�. According to the stoichiometry of the reaction, and combiningthis with the faraday value, 1 mg of water corresponds to 10.72 coulombs. It istherefore possible to directly determine the amount of water present in a sampleby measuring the electrode current in coulombs instead to measure the volumeof KF reagent as in the volumetric technique.

Magneticstirring bar

Anode of iodinegenerator

Cathode of iodinegenerator

Double platinumtip electrode

Iodine generatorelectrodes

Catholyte

AnolyteMembrane

II–

i > 0

+–

e–

oxidation of iodide (I–) at the contactof the working electrode (anode)

Figure 20.14 Karl Fischer two-component coulometric cell. Model DL-37 reproduced courtesyof Mettler Toledo. The instrument generates iodine by a electrolysis current applied in pulses.The duration of these pulses is reduced as the titration end point is approached. The diaphragmis used to avoid oxidation of the reduced ions appearing at the surface of the cathode. Somemodels exist without a diaphragm. They are easier to clean but they cannot solve all applications.


Commercial coulometers display the titration results as micrograms of water ordirectly in ppm or percentage water.

Similar to all other KF reagents, coulometric reagents deteriorate with temper-ature and light. This is why this reagent is commercially available from themanufacturers in two distinct bottles: one containing a mixture of sulfur dioxide,methanol and base, the other containing an iodide in solution. The contents aremixed prior to use.

Problems

20.1 1. Polarography is considered, so far as the sample is concerned, as anon-destructive method of analysis. Is this true?

2. Why is stirring of the solution avoided in polarography?

3. The method of standard additions is considered as yielding more reliableresults than that of standard solutions. Why?

4. Why, for the dropping mercury electrode, does the height of the columnof Hg have an influence upon the value of the current of diffusion?Upon what is this effect based?

20.2 In a polarography experiment, an aqueous solution containing a concen-tration of 10−3 M Zn�NO3�2 employs 0.1 M KCl as an electrolyte medium.

Calculate the ratio of the intensities of migration and diffusion for theZn ion in the proximity of the cathode.

Ionic mobilities Zn++ = 5�5 × 10−8, NO−3 = 7�4 × 10−8, K+ = 7�6 × 10−8

and Cl− = 7�9 × 10−8 m2 V−1 s−1.

20.3 A dropping mercury electrode is regulated such that one drop falls every4 seconds �t = 4 s�. The mass of the Hg corresponding to 20 drops is of0.16 g. Calculate the average mass flow of Hg in mg/s.

If the flow is proportional to the height of mercury in the reservoir, whatwould happen to the lifetime of the drops if the height of Hg was increasedthree-fold?

PROBLEMS 485

20.4 Calculate the average current of diffusion iD for the ion Pb2+ present as aconcentration of 10−3 M in 0.1 M KCl aq. at 0 �C.

Given: m = 2�10−3 g/s, t = 4 s, D = 8�67 × 10−6 cm2 s−1.

20.5 A solution of 1 M KCl, employed as an electrolyte support, is ready to useand contains 0.0001% of Zn. Is this solution richer in zinc than one of 1 Mwhich is prepared by using crystallised KCl for which the content in Zn isof 0.0005%?

20.6 A sample of 25 mL prepared for an electrolysis experiment has a zincconcentration of approximately 2 × 10−8 M which leads to the passage ofa current of 1.5 nA. Calculate the time necessary to deposit 3% of the Znpresent.

Show that the technique of stripping is more sensitive.

20.7 In order to measure the quantity of water in powdered milk by the methodof Karl Fischer method, the reactant is first standardised as follows:

15 mL of a solvent comprising methanol and formamide is introducedinto a cell. 3 mL of KF reactant is added to attain the equivalence point.

Then, 205 mg of oxalic acid dihydrate is introduced. A further aliquot(13 mol) of KF reagent must next be added to attain a new equivalencepoint. Finally 10 mL of the same solvent containing 1.05 g of dissolvedpowdered milk is introduced. Again KF reagent (12 mL) is added to find afinal equivalence point.

Calculate the % mass of water in the powdered milk.

20.8 Calculate the % mass of water in a portion of anhydrous ether knowingthat 1 coulomb is required to attain the equivalence point from 1 mL ofether during Karl Fischer measurements (coulometric version). Recall thattwo atoms of iodide per molecule of H2O are needed and that the densityof ether = 0.78 g/mL.

20.9 Determine the % impoverishment of a solution of 20 mL, 1 × 10−3 M zincnitrate during a measurement of five minutes by polarography. The strengthof the current in the circuit is 15�A.

21Sample preparation

For all chemical analyses, the analyte, which refers to the species to be measured,must be in a sufficient quantity and suitable form for the instrument used. Themajority of samples require a specific pretreatment. This preliminary stage, whichconditions instrument calibration and follows the so-called sampling procedure,has long been the ‘bottleneck’ in the analytical process. It is often a critical stepin a chemical analysis, because it have an influence upon the end result. Samplepreparation is therefore an essential step in analysis, as important as the measure-ment itself, greatly influencing its reliability, its accuracy and its cost. Since traceanalyses (less than 1 ppm of analyte in a crude sample), now represent at leasthalf of all analyses being performed, then powerful methods of extraction arerequired. The particular mode of enrichment is determined by the instrument orthe methodology used. This domain is currently very actively studied and benefitsfrom recent knowledge in robotics to shorten the time of preparation. Moreover,the large number of analyses of very small samples has stimulated the develop-ment of state-of-the-art equipment and up-to-date procedures, some of whichare described in this chapter, dedicated to samples intended for chromatographicanalysis.

21.1 The need for sample pretreatment

In order to start an analysis, a sample representative of the batch under studyis required. This contains the species being studied called the analyte, mixed, ingeneral, with a variable number of other compounds which constitute togetherwhat is called the matrix. When measuring traces of an analyte within othercompounds thousands of times more abundant, there is a fear that interfer-ences between analyte and other compounds may occur. Even the best analyti-cal techniques cannot remedy problems generated by poor sample pretreatment.This makes essential a meticulous sample preparation. Since this supplementarywork is often tedious and time consuming (Figure 21.1) methodologies involving


488 CHAPTER 21 – SAMPLE PREPARATION

Analysis(15% of time)

Results and reports(25% of time)

Sample preparation(60% of time)

Figure 21.1 Statistics displaying the proportion of the time spent in each stage of a chromato-graphic analysis. Sample preparation generally represents a large fraction of the total timededicated to the complete analysis (LC-GC Intl.1991, 4(2)).

adsorption, extraction or precipitation methods have been developed to make iteasier and when possible automatic.

� Measurement by atomic absorption at the mg/L level of elements in drinking wateror the scanning of a mid-infrared spectrum of a pure organic compound, as oftenperformed in a teaching laboratory, corresponds to simple situations for which thesample does not need a pretreatment. These conditions are not representative of thedifficulties encountered when working on real samples to be analysed. A pretreatmentbecomes essential.

21.2 Solid phase extraction (SPE)

SPE is currently used for the purification or concentration of a crudeextract prior to the measurement of one or several of its constituents. SPEis a clean analytical procedure which has drastically changed the classicalapproaches of solvent extraction as liquid/liquid extraction in a separating funnel,comparatively slower and that use relatively large amounts of liquid organicsolvents.

SPE operates in a small open plastic cartridge, similar to the barrel of a syringe,which contains an appropriate solid sorbent (e.g. a cartridge of 100 to 300 mg ofa RP-18 phase type) upon which the process consists of passing a known volumeof the liquid sample (Figure 21.2).

Two methods can be used:

• The currently most used method comprises an initial step in which thecompound of interest is retained by the sorbent-containing column, followedby the elimination, through rinsing, of the greatest possible number of unde-sired substances for the subsequent measurement. The analyte is then recove-red in a small volume of an appropriate solvent as a solution strongly enriched.This extraction procedure allows not only isolation of the analyte but also itspre-concentration, which is particularly useful in traces analysis.

• The second method, less frequently used, though very simple, consistsof passing the sample through the column in order that the undesired

21.2 SOLID PHASE EXTRACTION (SPE) 489

compounds are retained while the analytes pass freely. This approach is attrac-tive because it eliminates the elution (desorption step). On the other hand, theanalyte solution is purified, but not concentrated (enrichment factor of 1).

The solid sorbents closely resemble to that of the solid stationary phases of liquidchromatography. Bonded silica gels (of reverse phase polarity) with a particlesize of between 4 and 100�m, allow a percolation of faster flow rate. Otheradsorbents, containing graphite or co-polymers such as styrene-divinylbenzene oflarge functional group bonded surfaces, are more stable in acidic solutions.

b c d ea

Caffein

Solvent

0 4 8

min

Preparation Adsorption Rinsing Elution

Figure 21.2 Solid phase extraction. The separation of an analyte from the matrix. In thisexample the analyte is the only compound retained on the cartridge. Note the following steps:(a), (b) activation and rinsing of the sorbent prior to use; (c) introduction of a known volume ofthe sample; (d) interference elimination by rinsing; (e) desorption of the analyte by percolation.On the right, chromatogram (GC) obtained following treatment by this sequence of 1 mL ofcoffee. Below, on the left, SPE cartridges with reservoirs of 1 to 3 mL ; on the right, automatedsample preparation (Aspec model XL4 reproduced courtesy of Gilson).


There are also extraction discs (0.5 mm thickness and 25 to 90 mm in diameter)used as a kind of chemical filters in the same way as filter paper fit in the funnelof a vacuum flask. The discs are made of bonded phase silica particles trapped ina porous Teflon or glass fibre matrix. They retain traces of organic compoundspresent in large volumes of aqueous solutions, something that is not possible withthe cartridges described above. The analyte is recovered by percolating a solventthrough the filter. Trace analysis is made easier because the enrichment factor canbe as high as 100.

Non-polar compounds are isolated from a polar matrix with a cartridge or adisc of C-18 derivatized silica gel. Polar compounds are isolated from a non-polarmatrix with a cartridge filled with a normal phase. Charged species can be isolatedon an ion exchange phase. These three situations are well adapted to analysis byHPLC.

Two particular points require attention. During the extraction step the break-through volume must not be reached since beyond this amount the compoundto be extracted will no longer be trapped by the cartridge. Elsewhere, during thepercolation step, the recovery of the compound absorbed is rarely complete. If themeasuring technique calls upon detection by mass spectrometry this quantificationproblem can be resolved by introducing, prior to extraction, of a given volumeof the sample, a known quantity of this same compound labelled with a stableisotope. The behaviour during this sequence of the two forms of the compoundbeing the same, the comparison of their respective signals will permit the estab-lishment of their ratios and consequently the concentration of the unknown. Thisis the equivalent of the method of internal standards using a standard for whichthe relative response coefficient will be 1 (cf. paragraph 4.9).

A current research theme concerns the preparation of adsorbents having amarked affinity for a particular type of compound. For this, polymers aresynthesized which possess recognition sites in the form of surface deforma-tions, appropriate for trapping molecular targets. The principle resembles thatof immuno-extraction, which is even more selective, as explained in the nextparagraph.

� In conventional liquid/liquid extraction, the analyte is diluted in a large volume ofsolvent. Consequently, when the extracted solution is concentrated, so too are thenon-volatile impurities contained in the solvent. This frequently makes the methodunacceptable unless ultra-pure solvents are used. For example, if 1 mg of analyteis mixed with 1 mL of 99.9 per cent pure solvent, this latter brings a mass of addedcontaminants equal to that of the analyte.

21.3 Immunoaffinity extraction

Retention of the analytes with classic SPE cartridges is based upon hydrophobicinteractions. This method can lack selectivity if the matrix in which the targetanalyte is, contains interferent compounds of which greater concentration is

21.4 MICROEXTRACTION PROCEDURES 491

much that are likely to interfere. A lot of progress have been made in devel-oping new types of cartridges based on immunoadsorbers, able of an effi-cient enrichment of a single analyte from complex environmental matrices. Thismolecular recognition is based upon the interactions of antigen/antibody type(cf. Chapter 17).

By fixing through covalent bonding an antibody on an adapted solid support,it will result a sorbent that will fix the corresponding antigen, as a molecu-larly imprinted polymer (Figure 21.3). Immunoaffinity techniques, now usedextensively in pharmaceutical and biotechnology applications, can be adapted toextract small organic molecules of environmental samples. There exist extrac-tion cartridges containing antibodies of herbicides or polycyclic aromatic hydro-carbons (HPA) adapted to the extraction of these compounds by a rapidpercolation.

As already reported, extraction yield does not attain 100 per cent. For immuno-extraction there can be an insufficient number of active sites. It is thereforeindispensable to introduce a known amount of a tracer.

21.4 Microextraction procedures

21.4.1 Solid-phase microextraction (SPME)

SPME integrates sampling, extraction, concentration and sample introduction intoa single solvent-free step. This technique uses a 1 to 2 cm long segment of porousfused silica fibre coated with an appropriate adsorbent material. This fibre is heldin a syringe-like device, protected by the steel needle (Figure 21.4). The device’splunger is depressed to expose the fibre to the sample then retracted at the end ofthe sampling time (the fibre may be introduced into the aqueous solution or inthe space situated above it surface (‘headspace’, cf. Section 21.6). This process does

1 2 3 4

sample

Figure 21.3 Principle of immunoaffinity extraction. The different steps of a classic procedureon a cartridge containing the immobilized antibodies adapted, on this illustration, to the squaremolecules. After the fixing step (2), rinsing (3), then elution (4) of the analyte is done with anorganic solvent.


Solvent dropAqueous solution

Microsyringe

(b)(a)

detail onthe coated tip

L = 1 cmDiam = 70 µM

Figure 21.4 Micro-extraction procedures. (a) Micro-extraction using an adsorption fibre;(b) Micro-extraction with a single drop of organic solvent. Advantages of this technique are:ultra small volume of sample, low chemical consumption and fast analysis (reproduced courtesyof Supelco).

not need solvents. The sample analytes are directly extracted and concentratedon the extraction fibre. Then the fibre is introduced into a particular injector ofa GC, where, through the effect of the temperature, the compounds of interestare desorbed and then separated. The SPME technique can also be routinely usedin combination with HPLC, HPCE and MS. Sensitivity is usually low-to-mid pertrillion, but this procedure is rather expensive despite the same fibre can be usedaround 50 times.

21.4.2 Liquid-phase microextraction (LPME)

This technique also called single-drop microextraction, operates in a two-phasemode. Analytes are extracted from 1 to 4 mL aqueous samples into 25–50�Lof an organic very pure solvent, as hexane. It uses a microdrop of solvent atthe tip of a conventional microsyringe, rather a fragile silica fibre as above. Themicrodrop, formed at the point of the syringe needle, is immersed over severalminutes into the aqueous sample solution containing the products to be extracted(Figure 21.4b). LPME combines extraction and concentration in one step. Subse-quent analysis is performed by GC. Quantification is possible, provided operatingconditions are held constant through all of the calibration procedure. The methodhas been applied to the analysis of chemical solvents in foods and pharmaceuticals,natural plant components, environmental volatile and semi-volatile contaminantsin water.

The purification of small quantities of aqueous solutions traditionally performedusing a separating funnel (liquid-liquid extraction) can be carried out advanta-geously by a small column containing a porous chemically inert material which isstrongly water adsorbent. The aqueous sample is first absorbed into the column(the size must be such that all of the solution should be absorbed). At this stage

21.5 GAS EXTRACTION ON A CARTRIDGE OR A DISC 493

the water diffuses into the inert material and behaves as an immobile film ofaqueous phase that permits the neutralization and washing the aqueous phasewith a non-miscible solvent.

21.5 Gas extraction on a cartridge or a disc

In order to measure low concentrations of molecular compounds presentin gaseous samples, for example a polluted atmosphere, the best methodconsists of trapping them by passing a known volume of the sample througha short tube of absorbing material or through a disposable SPE cartridge(Figure 21.5).

The composition of the trap-column is variable: molecular sieves, graphite-based carbon black, organic polymers. A trap can be composed of a series ofseveral adsorbents. A pump rate is used to deliver a pre-programmed volume ofgas, in relation to the capacity of the trap (flow rate of 0.1 to 1 L/min).

0 1 0 2 0

2 - Graphite (for small molecules)3 - Molecular sieves (for light compounds)

0 - Glass wool1 - Graphite (for large molecules)

Testing tube ORBO 24

909300-0118/0119

oxazolidines of:1 - Ethanal2 - Methanal3 - Acrolein (3 ng)4: 2-(Hydroxymethyl)piperidine in excess

R CO

H

NH

CH2OH

N

ORH

–H2O

0 8 12 16 20

Min

4

4

2

Blank

GC analysis

Sample

Aldehyde

4

Oxazolidine

32

1

0 3

4

Figure 21.5 Gas extraction. Also called the dynamic purge-and-trap method. Principle of agas/solid extraction column. A chemical transformation used to detect an aldehyde by deriva-tivization (testing polluted atmosphere, Supelco Inc.).


The compounds absorbed are recovered either through extraction by means ofsolvents (often using carbon disulfide), or by thermal desorption in a carrier gaswhich avoids analyte dilution and the introduction of artefacts.

This technique can be adapted to gas phase chromatography. The trap is insertedinto a special oven and heated with a temperature gradient able to attain 350 �Cin a few seconds. The desorbed compounds are directly introduced into the GCinjector. As an alternative to these special ovens there exists extraction tubes ofa diameter sufficiently small that can be directly introduced into a modified GCinjector.

The recovery of the compounds is considered to be satisfactory when it attains60 per cent, but it is often almost quantitative with this device.

� Purge and trap. The same extraction tube filled with several layers of adsorbentsenables the retention of a broad range of molecules with different polarities. Eachlayer protects the next, which is more active. The first layer serves to purge the sampleof heavy compounds. Lighter compounds and gases are adsorbed by the subsequentlayers. To regenerate the trap, the sweeping gas circuit is reversed, so that the highmolecular weight compounds retained at the entrance of the tube, are eliminated first(cf. Section 21.5).

A new range of problems appear, affecting more than 50 per cent of thesamples treated for trace analyses: absorption by the walls of the containers,action of atmospheric oxygen, evaporation of the analytes, etc. As a consequencethose methods are favoured which lead to an enhanced enrichment with a shortextraction time.

The same principles are applied for developing detector tubes, which contain,along with the adsorbent, a reagent that causes a specific derivatization of theanalyte. This can be a change in colour of the tube contents, the analyte beingnot extracted. Manual breath alcohol tests are found in this category. There nowexist many dosimeter badges used as personnel protection indicators in whichthe circulation of air in contact with the badge is effected naturally and not witha pump. The colour intensity is correlated to the concentration of gas and thetime of exposure. This is used for pollution control at places of work or in theenvironment. The flexibility of this method is due to the wide choice of adsorbentphases that permit selectivity of extraction. When molecules are unstable on theadsorbent and therefore would require stabilization, they can be transformed to aspecific derivative by a reagent mixed with the adsorbent.

21.6 Headspace

This relatively simple technique can provide sensitivity similar to the abovedynamic purge-and-trap analysis. Headspace is a sampling device used in tandemwith a GC installation (Figure 21.6). It is reserved for the analysis of volatilecompounds present in a matrix, which cannot be itself directly analysed by

21.6 HEADSPACE 495

chromatography. This is generally the case as most samples are composed ofa wide variety of compounds that differ in molecular weight, polarity, andvolatility. Basic principles of headspace are illustrated by the two followingvariations:

• Static mode: the sample (solid or liquid matrix) is placed in a glass vial cappedwith a septum such that the sample occupies only a part of the vial’s volume.After thermodynamic equilibrium between the phases present (1/2 to 1 h), asample of the vapour is taken. Under these conditions, the quantity of eachvolatile compound present in the headspace (volume above the liquid) willbe proportional to its concentration in the matrix. After calibration (usingmethods of internal or external standards), it is possible to match the realconcentrations in the sample with those of the vapours injected in the gaschromatograph (Figure 21.6).

• Dynamic mode: instead of working in a closed environment, a carrier gassuch as helium is either passed over the surface of the sample or bubbledthrough it in order to carry the volatile components toward a trap wherethey are adsorbed and concentrated (Figure 21.7). The procedure continueswith a thermal desorption of the trap using reversed gas flow in respect ofthe injection in the chromatograph. This ‘purge-and-trap’ principle is semi-quantitative and delivers a sample without residue.

Gas(headspace)

Sample(solution)

Sealed vial

Vg

Vs

K = Cs/Cg

Cs

Cg

volatile analyte

β = Vg/Vs

Figure 21.6 Static headspace. Sample vial in a state of equilibrium. The state of equilibriumis under the control of two factors: K = Cs/Cg and � = Vg/Vs. In addition to routine singleextraction (one sampling per vial), modes of multiple headspace extraction are incorporated inthis model G1888 (reproduced courtesy of Agilent Technologies).


Sample

Preparation of the trap

Sample extraction

a

a

b

b

c

Desorption of the trapc

GC

(GC for Gas Phase Chromatograph)

GC

GC

Trap

Figure 21.7 Headspace, dynamic mode. The sample is recovered by thermal desorption (strip-ping) of a purge-and-trap cartridge, chosen as a function of the compound to be extracted.

This method is quite reliable for repetitive analyses involving stable matrices.However, if the matrix composition fluctuates, then this disturbs the equi-librium factors and reduces the precision of the result, by consequenceof an irregular calibration. In this case cartridge-base extraction would bepreferred.

21.7 Supercritical phase extraction (SPE)

Extraction using a fluid in the supercritical state is a well-known procedureemployed in the food industry. Analytical extractors operate on the same principle.They incorporate a very resistant tubular container in which is placed the sample(in solid or semi-solid form) with the fluid (CO2, N2O or CHCIF2 – Freon22) inthe supercritical state. There are two modes of operation:

• Off-line mode consists of depressurising the supercritical fluid followingextraction. By returning to the gaseous state, it leaves the analytes in aconcentrated form with the undesirable impurities on the internal wall of theextraction vessel. The concentrate is dissolved using some classical solventand submitted to a selective extraction on a solid-phase cartridge.

• On-line mode consists of performing the direct analysis from the extract,while it is still under pressure, by passing the supercritical fluid through a

21.7 SUPERCRITICAL PHASE EXTRACTION (SPE) 497

chromatographic installation (SFC or HPLC). This procedure is applied onlyto those compounds for which interferences due to matrix are not likely tooccur.

In summary, SFE acts on four parameters that can be modified to obtain a goodselectivity: pressure, temperature, extraction period and choice of modifier. It isalso possible to change the solvation character of the fluid by the introduction ofan organic modifier (e.g. methanol, acetone). Nonetheless, to separate the analytefrom the matrix requires a knowledge of the solubility and transfer rate of thesolute in the solvent as well as of the physical and chemical interactions betweensolvent and matrix (Figure 21.8).

The use of microwaves combined with extraction by solvent in a pres-surized container is another very efficient process for the rapid treatmentof samples.

7 MPa Pressure 70 MPa

CO2CO2

CHCIF2

N2O

T = 31°C

T = 150°C

Hildebrand scale

Fluid CriticalPoint (°C)

Dipole moment(Debye)

Supercritical Fluid Properties

32

37

96

0

0.2

1.4

AcetoneDichloromethaneBenzeneEtherHexane

Figure 21.8 Supercritical fluid extraction. Comparison of the solvation strength of the CO2

with respect to the usual solvents (Hildebrand scale) as a function of the temperature andpressure. The polarity of carbon dioxide in the supercritical state is comparable with that ofhexane (for 100 atm and 35 �C). SPE is a method for which automation becomes a justifiedinvestment when the sample throughput is large. Above, sample extractor by supercritical fluids(Model SFE-703 reproduced courtesy of Dionex).


21.8 Microwave reactors

The transformation to elements of samples containing organic material, known asmineralization, has motivated the development of many different approaches: dryprocedures such as oven heating, combustion, while others by wet treatment suchas with mineral acids, fluxes for fusion, etc. In the absence of a universal methodapplicable to all inorganic elements, the mineralization must be adapted to thesample. This indispensable step of the preparation of a large number of samples,in particular for those analysed by AAS and OES, can be made easier by using ofa ‘microwave digester.’

� Mineralization by strong acids conducted in open containers, in a fume-hood, withthe ever present risk of cross contamination and ‘bumping’, is a long and fastidiousoperation which fundamentally has changed little over a century. Beyond the practicalproblems involved, some sample matrices are quite impossible to treat under theseconditions (refractory or volatile materials, certain minerals, charcoals and heavyoils).

Microwave digesters consists of a Teflon ‘bomb’ of a few mL volume in whichthe crude sample is placed along with the mineralization solution (necessary forcarbonization or oxidation). The heating, induced by the microwaves, occursvia molecular agitation due to the dipoles of the water molecules. The closedcalorimetric-type vessel avoids losses through droplets or aerosols, or evaporationof volatile components and splashing. The temperatures reached by the acidicsolutions under pressure quickly exceed the boiling temperatures under normalconditions (the same effect is seen in a pressure-cooker). This gain in time hasbeen known, in certain cases, to reach more than 90 per cent. In such condi-tions, digestions by sulfuric or perchloric acids, hydrolyses or mineralizations ofKjeldhal in oxidizing media can be performed. This system can be automatedquite safely.

21.9 On-line analysers

All of the laboratory instrumental methods have been practically adapted foron-site analytical procedures, from pH measurement to NMR analyses. The instru-ments are generally less versatile than their laboratory counterparts. Dedicatedto particular measurements and suitable for harsh environments or hazardousareas, they must be robust, so their design is different. They are configured forindustrial process control. Many of them are process analysers for concentrationmeasurements. A continuous sample is introduced via a diaphragm pump into asmall tank. At intervals the sample or calibration standards are pumped into the‘chemistry stream’ where they are treated depending of the method of analysis(UV, IR).

21.9 ON-LINE ANALYSERS 499

Analyser

Analyser

Reactor

Reagents

a b

ComputerComputer

Product

Figure 21.9 The two control procedures for on-line analysis. Taking a chemical reaction as anexample, procedure (a) corresponds to an analyser situated after synthesis (closed loop feedbackthrough comparison with a reference value). Alternatively, procedure (b) corresponds to anup-stream analyser (in an open loop with continuous adjustment of the reagents’ composition).

In this type of analysis, the result must be obtained rapidly as a strategy offeedback is used to optimize or to ensure the stability of the operation. The on-lineanalyser can control the procedure either up or down stream of the reactor(Figure 21.9).

The use of a selective sensor plunged into the centre of a product to be analysedis not always possible. The preparation of the analyte prior to measurement leadsto the removal of a small fraction in order to ensure that the applied treatment isadequate.

22Basic statistical parameters

In chemical analysis, as in many other sciences, statistical methodologies areunavoidable. The calibration curve constitutes an everyday application, just as ananalytical result can only be ascertained if an estimation of the possible error hasbeen considered. Once a measurement has been repeated, a statistical exploitationbecomes possible. However, the laws of sampling and tests based upon hypothesesmust be understood to avoid non-value conclusions, or to ensure the meaningfulquality tests. Systematic errors (user-based, instrumental) or gross errors whichlead to results beyond reasonable limits do not enter into this chapter. For thetests most frequently met in chemistry only indeterminate errors are consideredhere.

22.1 Mean value, accuracy of a collection ofmeasurements

When n measurements are repeated upon the same sample (in the chemical senseof the term) and particularly to a high degree of precision it is frequently foundthat individual values differ slightly within the group. In these cases a preferencefor an estimation of the final result based upon the arithmetic mean x is expressed.This mean x of the n measurements is obtained from expression 22.1. This meanis accepted as being better than any individual measurement taken at random:

x = x1 + x2 + � � � + xn

n=

∑xi

n(22.1)

An alternative to the mean or average value, though more rarely used in chemicalanalysis, consists of taking the median: after having classed the values in increasingorder, this is the result situated in the middle of the series, except when thenumber of the series is even in which the average of the two middle numbersis taken. The median has the advantage of not giving any particular weight toany abnormal value. For example if the values are 12.01, 12.03, 12.05 and 12.68,the arithmetic mean is 12.19 and the median 12.04, a value certainly better than


502 CHAPTER 22 – BASIC STATISTICAL PARAMETERS

the mean as it does not take into account the last value in the example given,which appears to be abnormal (dispersion 0.67). The median is a non-parametricstatistical method (Section 22.8).

The mean value is impossible to know in advance as the measurements arerandomly variable. However, it is not by repeating the same measurement a greatmany times and finding values with little difference between them that the centralvalue is rendered close to the exact value, equally called the true value x0, (at thisstage unknown) because of the possible existence of systematic errors.

Each measurement x must be considered as the sum of the true value x0 andan absolute experimental error value �. The absolute error �i of measurement i isthus expressed as:

�i = xi − x0 (22.2)

If n becomes very large, as in the case of a statistical population, the mean xbecomes the true mean � and be confused with the true value x0 in the absenceof systematic errors. This assumes that the measurements follow the Normal orgaussian distribution (see Figure 22.2).

If the true value x0 is known (e.g. analysis of a standard of perfectly knowncomposition), the accuracy of the result or of the method used is characterized bythe total systematic error � calculated from the true mean as follows (cf. Table 22.1and Figure 22.1).

� = � − x0 (22.3)

Table 22.1 Examples of results from an analysis grouping the various parameters of expressions22.1 and 22.2 ( the true value is x0 = 20)

Chemist 1 2 3 4

Measurement 1 20.16 19.76 20.38 20.08Measurement 2 20.22 20.28 19.58 19.96Measurement 3 20.18 20.04 19.38 20.04Measurement 4 20.2 19.6 20.1 19.94Measurement 5 20.24 20.42 19.56 20.08Mean x 20.2 20.02 19.8 20.02Median 20.18 20.04 19.38 20.04Systematic error � 0.2 0.02 0.2 0.02Relative error ER

(expression 22.4)0.01 or

1% or104 ppm

1 × 10−3

or 0.1%or1000 ppm

0.01 or1% or104 ppm

1 × 10−3

ou 0.1%or1000 ppm

Variance �s2� 7�84 × 10−4 0.1183 0.1772 3�6 × 10−5

Standard deviation (s) 0.028 0.344 0.421 0.006Comments on the results Precise not

accurateNotpreciseaccurate

Notprecise notaccurate

Preciseaccurate

22.1 MEAN VALUE, ACCURACY OF A COLLECTION OF MEASUREMENTS 503

19.2 19.4 19.6 19.8 20.0 20.2 20.4 20.6

1

2

4

3

x

x

x

x

s

s

s

s

1

2

3

4

xy

Figure 22.1 Graphical illustration of the data from Table 22.1. To illustrate accuracy andprecision the standard deviations have been calculated using formula 22.8. Note the differencesbetween the arithmetic means indicated on the graph by a short vertical bar and the corres-ponding median values, which are arrowed. For the results from chemists 3 and 4, the differenceis fairly large. Chemist 1 has committed very probably a systematic error. On the right, a classicillustration of the precision and accuracy depicted with the aid of a target. This image is lesssimple than it would appear because there remains an uncertainty in both x and y.

The relative error ER of a measurement (or on the mean value) correspondsto the ratio of the absolute value of the deviation corresponding to �i (or �), overthe true value. ER can be expressed as a percentage or in ppm.

ER = �x − x0�x0

�x for xi or x� (22.4)

If the true value x0 is not known, which is usually the case in chemical analysis,then the experimental error of the measurement i being ei, is calculated by replacingx0 by the mean x in 22.2:

ei = xi − x (22.5)

ei represents the algebraic difference between the mean and the ith measure-ment. The mean deviation d or mean of the differences, calculated over n measure-ments allows an appreciation of the precision:

d =∑ �xi − x�

n(22.6)

In the last expression absolute values of the experimental error are taken sincewith algebraic values, this parameter d would rapidly tend towards 0 as n increases.


22.2 Variance and standard deviation

The above precision (mean deviation) has however the inconvenience that it cannotbe interpreted statistically since both large and small individual deviations, thoughnot being equally probable, have the same weight. The summing of the squaresof the differences is preferred which leads to the most largely used definitionfor the precision (reproducibility) in statistics, known as the variance s2, which isestimated for a set of n measurements by:

s2 =∑

�xi − x�2

n − 1(22.7)

The square root of the variance is the standard deviation, represented either, whenthe number n of measurements is small, by s or by � when a large statisticalpopulation of values is available (expression 22.8). The standard deviation is ‘adispersion index’ expressed in the same units as x.

Calculators and related programmable software possess the corresponding func-tions:

s = √s2 =

√∑�xi − x�2

n − 1(22.8)

For an infinite number of measurements, s is replaced by � , n is replaced byn − 1 and � is used instead of the arithmetic mean x.

To compare results or to express the uncertainty of a method, s is oftenexpressed in a relative manner. Calculations are made therefore of the relativestandard deviation (or RSD), also called coefficient of variation (CV) and mostoften expressed as a percentage:

CV = 100 × s

x(22.9)

� When the result of an analysis arises from a calculation involving many experi-mental values, each having its own standard deviation, there will be, by consequence,a propagation of errors. The precision of the result is calculated using simple equa-tions that are found in most introductory textbooks concerned with statistics.

22.3 Random or indeterminate errors

In the absence of systematic errors, accidental errors ‘due to hazards’, exist thatcannot be controlled because they are indeterminate. Their direction and ampli-tude varies in a non-reproducible manner from one measurement to another.A mathematical analysis of the error curve leads to the conclusion that the arith-metic mean x of the individual values is the best estimation of the true mean �(Figure 22.2).

22.3 RANDOM OR INDETERMINATE ERRORS 505

Fre

quen

cy

Experimental values

Measured values

f(X)

μ(2)μ(1)

s

s

2 31

– 2 – 1 0 1

y

x

2σ

normal Gaussian distribution

2

Figure 22.2 Gaussian curves. When the number of measurements increases and if the intervaldetermining the group is narrow, then the graphical shape will take (measurement/frequency)the form of a Gaussian curve (Normal distribution law). Below, two series of results centredon two different true means �. If the number of measurements is very small, it is not possibleto estimate the average distribution, thus the true mean. At the bottom right, a reduced formof the Gaussian distribution is shown. The reliability of the mean is given by the 95 per centconfidence interval.

The symmetry and appearance of this curve shows that:

• There are an equal number of errors, positive and negative, with respect tothe true mean value

• Small errors are more frequent than large errors

• The most encountered value is the true mean � (without error).

The normal distribution law (bell-shaped gaussian curve) is the mathematicalmodel which best represents the distribution of random or indeterminate errorsdue to hazards (Equation 22.10):

f �x� = 1

�√

2exp

[−�x − ��2

2�2

](22.10)

In order to make this expression universal, the true mean of a population �,is used for values of x and its standard deviation � for the unit of measure(Figure 22.2).

With X = x − �

�expression 22�13 becomes f �X� = 1√

2exp

[−X2

2

](22.11)


If the number of measurements is not very large it is important to know theirdistribution. The curve obtained yields information about the reliability Re of theresults. The reliability of the mean, as an estimation of the true value, increaseswith the square root of the number of measurements n.

Re = K√

n (22.12)

Thus, when the number of measurements n1 increases to a larger number n2,the reliability Re is improved by a factor k such that:

k =√

n2

n1

(22.13)

The distribution function is the integral to the function f �X�. This function issuch that 95.4 per cent of the area lies within an interval of width ±2� from thevalue of the true mean. Therefore the chances are 95.4 per cent that the errorassociated with a given measurement will be contained within the interval ±2� . Ahigh value for the standard deviation � signifies a broadened distribution curve.If the number of values is small (a few units), s must be taken instead to estimate� (Figure 22.2). The greater n is, the better will be the match.

Thus, s and x are estimations of � and of the true mean � which relates to thetotal population.

� In practice, it is not possible to know either the true mean � or the standarddeviation � since there will be a limited number of values of n. Thus s must becalculated. Elsewhere, when a large number of repetitive measurements concerningthe same sample is available, the Chi-square test for the standard deviation( 2 test) is used to ascertain if the frequency distribution (that is the number of timeswhere a value is recorded) differs in a significant manner from that of a population,which follows the normal distribution law. Without using proper software this test ofnormality is a lengthy calculation process.

22.4 Confidence interval of the mean

When the number of the measurements n is small (for example, if n is between4 and 15), and if there are no systematic errors, the true mean � can be quitedifferent from the arithmetic mean x. An estimation of the true mean must thenbe made by calculating a confidence interval within which a probability is given(for example 95 per cent), that the real value x0 will be included.

The confidence interval, around the mean x, in order that the true mean � iswithin (or x0 in the absence of all systematic errors), is given by the followingformula:

x − t · s√n

≤ � ≤ x + t · s√n

(22.14)

22.4 CONFIDENCE INTERVAL OF THE MEAN 507

In equation 22.14, Student’s coefficient t is a statistical factor, which depends uponn and of the level of confidence chosen. These values are displayed in Table 22.2.The greater n is, then the narrower will be this interval, s being the standarddeviation of the series of measurements.

Table 22.2 Values of the Student’s bilateral confidence coefficient t (calculation of Student’sdistribution)

n Level of confidence 90% Level of confidence 95% Level of confidence 99%

2 6�31 12�71 63�663 2�92 4�30 9�934 2�35 3�18 5�845 2�13 2�78 4�606 2�02 2�57 4�037 1�94 2�45 3�718 1�90 2�36 3�509 1�86 2�31 3�3610 1�83 2�26 3�2511 1�81 2�23 3�1712 1�80 2�20 3�1115 1�76 2�14 2�9820 1�73 2�09 2�8630 1�70 2�05 2�7660 1�67 2�00 2�66120 1�66 1�98 2�62

This confidence interval is calculated when a method of measurement is testedwith a sample for which the corresponding true value x0 is known, though itremains to be seen if the latter is situated in the confidence interval calculated.

This test of Student’s variable t can equally lead to an adjustment of the numberof measurements to be conducted in order to attain a result with the pre-selectedlevel of confidence.

If, as well as the mean x, the true value x0 (or the true mean �) is also known,expression 22.14 will permit the calculation of the value of t, according to thedegree of confidence chosen (expression 22.15 if n > 20, else 22.16). A value of tlarger than that indicated in Table 22.2, on the line corresponding to the value ofn, will be due to a systematic error.

t = �x − ��s

√n (22.15)

or

t = �x − x0��

√N (22.16)


In the formula, which leads to the calculation of confidence intervals, thestandard deviation of the mean sx, or the uncertainty of the standard deviationmay appear, using the following relation that gives the standard deviation of themean (22.17):

sx = ± s√n

(22.17)

22.5 Comparison of results – parametric tests

When it is required to compare the results of two methods, or of two instrumentsapplying the same analysis method, or of two laboratories upon the same sample, itis essential to refer to statistical tests. Two main families exist: parametric and non-parametric tests. The first supposes that data are distributed according to a Normallaw (on which the values in Student’s table are based), while non-parametrictests are based on so-called robust statistics, less sensitive to abnormal values. Inanalytical chemistry it is not often that large quantities of data are collected.Therefore statistical tests must be applied with judgment. They are associated withan acceptable margin of precision, for example 10 or 5 or 1 percent.

22.5.1 Comparison of two variances, Fisher–Snedecor Law

The comparison of the standard deviations s1 and s2 of two different sets of resultsis known as a test of the variance equality. In this test, the F factor, which is theratio of the two variances is calculated in order that F > 1:

F = s21

s22

(22.18)

The null hypothesis (statistical terminology), states that if there are no significantdifferences in the variances, then the ratio must be close to 1. Reference shouldtherefore be made to the Fisher–Snedecor values of F , established for a variablenumber of observations (Table 22.3). If the calculated value for F exceeds thatfound in the table, the means are considered to be significantly different. Sincethe variability s2

1 is greater than s22, then the second series of measurements is

therefore the more precise one.The adaptation of this test for robust statistics (non-parametric tests) requires

simply to calculate the ratio F =R1/R2 from the two distributions (the differencebetween the two extreme measurements) of the two series under comparison.

22.5 COMPARISON OF RESULTS – PARAMETRIC TESTS 509

Table 22.3 Summary of the F threshold values established for a confidence level of 95per cent

Number of measures(denominator)

Number of measures (numerator of the fraction F )

3 4 5 6 7 10 100

3 19�00 19�16 19�25 19�30 19�33 19�38 19�504 9�55 9�28 9�12 9�01 8�94 8�81 8�535 6�94 6�59 6�39 6�26 6�16 6�00 5�636 5�79 5�41 5�19 5�05 4�95 4�78 4�367 5�14 4�76 4�53 4�39 4�28 4�10 3�6710 4�26 3�86 3�63 3�48 3�37 3�18 2�71100 2�99 2�60 2�37 2�21 2�09 1�88 1�00

� Amongst the examples in Table 22.1 there is no significant difference between theresults of chemists 2 and 3 for a degree of confidence of 95 per cent. An experimentalvalue of F = 1.5 is obtained using equation 22.18, which is less than the tabulatedvalue of F = 6.39 for five measurements made by each chemist. In fact, F = 1.5while from the data in Table 22.1 F = 6.39. This verifies that their standard deviationsare not significantly different.

22.5.2 Comparison of two experimental means, x1 and x2

Sometimes it is desirable to compare the means obtained from two series ofmeasurements to consider if they are significantly different, bearing in mindthat the true value is unknown. Initially it must be determined whether thereis any significant difference with respect to the precision of the two means (cf.Section 22.5.1). Next, a calculation using expression 22.19 for the global or pooledstandard deviation sp is performed. Then the corresponding value for t is calcu-lated using equation 22.20. It is compared to tabulated value for n = n1 + n2 − 2measurements and for the degree of confidence chosen. If the value of t in thetable is greater than the value calculated, then it can be concluded that these twomeans are not significantly different.

sp =√

�n1 − 1�s21 + �n2 − 1�s2

2

n1 + n2 − 2(22.19)

t = �x1 − x2�sp

√n1n2

n1 + n2

(22.20)


22.5.3 Estimation of the detection limit of an analyte

The two expressions 22.19 and 22.20 are useful for estimating the smallest concen-tration of an analyte that can be detected, but not quantified with a pre-selectedlevel of confidence. One of the two means (x2 for example) is considered to bethe result of a set of measurements made on the analytical blank. It will be notedas xb with a standard deviation of sb. If n1 = 1, then expression 22.19 simplifies tosp = sb, leading to expression 22.21 (using a t value extracted from Table 22.2 forn1 + nb − 2):

�x = x1 − xb = ±t · sb

√n1 + nb

n1 · nb

(22.21)

� If six measurements are undertaken upon an analytical blank leading to a standarddeviation of 0.3 � g for the measurement considered, then – with expression 22.21and for a degree of confidence of 99 per cent, – a value of 1.31 � g will be calculatedas the detection limit if only a single measurement is made and a value of 0.59 � gif five measurements are made �xb = 0). Empirically it can be admitted that theinstrumental detection limit corresponds to the concentration which leads to a signalwhose relative intensity (central value x) is twice the standard deviation calculatedfor 10 measurements of the analytical blank (degree of confidence 95 per cent). Thelimit of quantification is always higher.

22.6 Rejection criteria Q-test (or Dixon test)

Sometimes, a value within a set might appear aberrant. Although it might betempting to reject this data point, it must be remembered that it is only abnormalin respect of a given law of probability. There exists a simple statistical criterionfor conservation or rejection of this outlier value. This is Dixon’s test, whichconsists of calculating the following ratio (on condition that there are at leastseven measurements):

Q = �value in question − its closest neighbour�largest value − smallest value

(22.22)

Q calculated in this manner is compared with a table of critical values of Q as afunction of the number of data (Table 22.4). If Qcalculated is greater than Qcritical thevalue in question can be rejected.

� Note: The ASTM standard (American Society for Testing Materials) uses a differenttest for rejection of an outlier, called the reduced central value zi = (xi − x/s), whichhas its own table of characteristic critical values.

Henry’s curve, the principle of which is available in more advanced statistical texts,also constitutes a good method for detecting outliers using a visual approach.

22.7 CALIBRATION CURVE AND REGRESSION ANALYSIS 511

Table 22.4 Tabular summary of critical values for Q (Dixon’s test)

Number of measurements, n Confidence level 95% 99%

3 0�94 0�994 0�77 0�895 0�64 0�786 0�56 0�707 0�51 0�648 0�47 0�599 0�44 0�58

10 0�41 0�53

22.7 Calibration curve and regression analysis

Instrumental quantitative analysis is commonly based upon comparative methods.For example the sample that contains the analyte and a standard which contains thesame concentration of this analyte will yield identical signals, using an instrumentwith the same settings. In the majority of cases, a series of standards of knownconcentrations are measured, rather than a single one. Then a calibration orworking curve is drawn from the values of the analytical signal as a functionof analyte concentration. This calibration curve is then used to determine theconcentration of an unknown sample or to calibrate the response of the usedinstrument. Traditionally, on the graph, abscissa corresponds to the concentrationand ordinate of the signal value.

The purpose of regression analysis as used in quantitative analysis is to generatean equation that relates signals to concentrations, such that if we are given aparticular value of a signal we can get the unknown concentration. Therefore,regression analysis takes a step beyond correlation, allowing creation of a predictivemodel between two (or more) variables. In other words the signals yielded bythe instrument (y-axis) are modelized as a function of concentration (x-axis). Amodel is adopted Y = f �X� allowing an evaluation of y since x and the functionare known. Therefore the uncertainty of the results is an accumulation of theuncertainty linked to the measurement and also to the model chosen for thefunction. Quantitative analysis software uses numerous calculation models. Hereonly the principal results are given concerning the simple linear regression, thestatistical approach most frequently met in quantitative analysis (Figure 22.3).

22.7.1 Simple linear regression

As the response of many detectors is linear as a function of the measured variable,taking account of the differences due to experimental conditions as well as of theinstrument, the goal is to find the parameters of the straight line that best fits.


50 10 15 20 25 30

Concentration (mg/l) X

YA

bsor

banc

e

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

R2 = 0.9712

Regression line:Y = 0.0264X + 0.0161Thiel’s lineY = 0.0260X + 0.010

Figure 22.3 Linear regression and the Thiel’s line (Section 22.8) corresponding to the data ofTable 22.5. Though in close proximity the two lines lead to different results. For example, fory = 0�5, leads to x = 18�85 (Thiel) and x = 18�33 (linear regression), a difference close to 3per cent. Spreadsheets will often have built-in regression functions to find the best line for a setof data.

The least squares regression line is the line which minimizes the sum of the squareor the error of the data points. It is represented by the linear equation y =ax + b.The variable x is assigned the independent variable, and variable y is assigned thedependent variable. The term b is the y-intercept or regression constant (the valueof when x = 0), and the term a is the slope or regression coefficient.

Coefficients a and b, as well as the standard deviation on a, may be given byseveral formulae and specialized software.

Moreover, the dimensionless Pearson correlation coefficient R gives a measureof the reliability of the linear relationship between the x and y values. If R = 1 itexists an exact linear relationship between x and y. Values of R close to 1 indicateexcellent linear reliability. If the correlation coefficient is relatively far away from1, the predictions based on the first order relationship, y = ax + b will be lessreliable.

a = n∑

xiyi −∑

xi

∑yi

n∑

x2i − �

∑xi�

2(22.23)

b =∑

yi − a∑

xi

n(22.24)

R = n∑

xiyi −∑

xi

∑yi√[

n∑

x2i − �

∑xi�

2] · [n∑y2

i − �∑

y�2] (22.25)

22.8 ROBUST METHODS OR NON-PARAMETRIC TESTS 513

A straight line supposes that the errors in y follow the law of Normal distribu-tion. R2 is the determination coefficient that conveys information about how thevariations of x overlap variations in y.

In classic calculations the experimental error is considered to affect the y valueexclusively and not the concentration recorded in x. If this is not the case, thedata points will not have the same quality for the regression line hence comes theidea of according less value to data more distant from the line. Through iterativecalculations the equation of a straight line is reached which takes account of theweighting of each point.

In order to compare whether two methods of analysis are highly correlated, aseries of n standards of different concentrations are analysed by two pathways.Each standard is next represented by a point on a graph where x bears theresults of method 1 and y the corresponding results from the second method. Thecorrelation coefficient R is determined and formula 22.26 is applied. If the t valueobtained is greater than the value found in the table for n− 2 degrees of freedom,there is a strong correlation between the two analytical methods.

t = R

√n − 2

1 − R2(22.26)

22.7.2 Multiple linear regression

Analysis by multiple linear regression leads to the prediction of a result (the depen-dent variable) when it depends upon a certain number of factors (the independentvariables). Software allows this type of calculation in which the contribution ofeach factor is determined using standards. The prediction of the result is calcu-lated by a general formula, such as 22.27 and as a composite of three factorsin x:

y = a + bx1 + cx2 + dx3 (22.27)

� For example, the protein content in cheese, related to the nitrogen percentage(result), can be established from the IR absorbance measured at differentwavelengths. This method is equally useful for calculating the parametersA, B and C of the van Deemter equation (Section 1.10), corresponding toexperimental data.

22.8 Robust methods or non-parametric tests

The statistical tests developed above assume that the data follow the Normaldistribution. However, there are analytical methods for which the results reveal


different distributions. Otherwise they are asymmetric, or symmetric but ‘non-normal’. On some approaches, these distributions are considered as resultingfrom the superimposition of a normal distribution and abnormal points. Theuse of the median (cf. Section 22.1), rather than the arithmetic mean, is partof this alternative approach. The standard deviation is replaced by the meandeviation MD.

MD =√

2·∑ �xi − x�

n(22.28)

Under such circumstances, the calibration curve can be reconsidered, as seenin the following example, which illustrates Thiel’s method (Table 22.5 andFigure 22.3).

In order to estimate the best straight line for a series of seven data points�x� y� in a colorimetric titration, the method consists first to rank the x valuesin increasing order. Since the Thiel’s method requires an even number of datapoints the median value must be rejected in this example. Then the calculation isthe following:

At first, the slopes of three straight lines are calculated, which pass respectivelythrough the first point and that following immediately the median and so on(Table 22.5). The median of the three calculated slope values is taken as the terma of the linear equation. Then, the six b values are calculated from bi = yi − axi

and also ranked in increasing order. The median will become the term b ofthe line.

Table 22.5 An example of determination of the linear equation coefficients usingThiel’s method from a set of seven data points

1 0

5

10

15

20

25

30

2

3

4

5

6

7

Entry#

Conc.(x )

Abs.(y )

0.02

0.14

0.25

0.39

0.65

0.66

0.77

slopes aij Term bi Classification

0.02 –0.01

0.01 –0.01

–0.01 0.01

0,13

0.01

–0.01 0.13

0.02

0.01

Equation of line Y = 0.0260X + 0.010

0.0320.026

0.026

22.9 OPTIMIZATION THROUGH THE ONE-FACTOR-AT-A-TIME (OFAT) EXPERIMENTATION 515

In chemistry this method should be more widely used when the number ofmeasurements is too small to be sure of the normality of the distribution.

Three advantages of Thiel’s method merit to be highlighted:

• it is not assumed that all of the errors are in y

• it is not assumed that the errors follow the Normal distribution law

• it is to be noted that an aberrant data does not affect the final parameters ofthe linear equation.

22.9 Optimization through the one-factor-at-a-time(OFAT) experimentation

When a measurement depends upon a signal (absorbance or intensity of fluores-cence) which is itself influenced by several factors, then in general, it is customaryto seek overall conditions which will lead to the maximum signal.

If the factors involved in an analysis are independent (which is rarely thesituation), a common practice is to experiment with one factor at a time whileholding all others fixed, then the influence of each one can be studied on theresult by using a simple repetitive method.

However, the results are often misleading and fail to reproduce conclusionsdrawn from such an exercise. This method needs some understanding of basicdesign of experiments (DOE) principles.

Imagine that a value given by a sensor depends upon two independent factorsx and y. After having fixed the factor x to the value x1 the influence of factor y onthe signal is studied (the signal is measured in the third dimension). For the valuey = Y1 it is observed that the signal passes through a maximum. This Y1 value isthen selected and then x is varied in order to optimise its value, which is x = X2

(Figure 22.4). Generally by repeating this procedure a new couple �X�Y� is foundwhich gives slightly improved values each time.

This repetitive method is attractive, as it is simple and supported by commonsense, but it does not always constitute the best approach to the problem. Ifthe iso-response curves form a complex envelope, showing notably a ridge –the mathematical illustration of the interaction between the two factors – thepreceding method can lead to a false optimum depending upon the parame-ters selected at the beginning. A more effective method for these situations isto study their effect simultaneously by setting the DOE statistical technique.This different approach has the aim of discovering the optimal conditionsusing the minimum number of attempts. This is illustrated by the sequentialsimplex method of optimization and by different designs described in specializedtextbooks.


Factor x

Fac

tor

y

Fac

tor

y

y

x1 x Factor xx1x2x3

Y1

Y2

Y3

123

(a) (b)

Figure 22.4 The ‘one factor at a time’ method. If there is a surface of continuous response,the iso-response curves have will lead to a variety of optimum situations.

Problems

22.1 The true value of a particular measurement is 131�9 g/L. Four chemists(A, B, C and D) each repeat the same procedure five times. The individualvalues obtained are displayed in the table below. Comment upon theseresults in terms of accuracy and precision (use an indicator of dispersionor standard deviation, s).

Chemist A 130�7 131�6 133�5 132�3 132�6 129�1Chemist B 125�0 132�3 136�9 137�9 125�9 131�6Chemist C 136�7 134�5 134�1 135�4 136�0 137�6Chemist D 130�7 109�9 131�9 115�6 131�3 132�6

22.2 With a column whose stationary phase is of squalane and under differingconditions of use, the following values for the Kovats factor of benzene(recognised average value = 653) were determined: 650, 652, 648, 651 and649. For the value of 653 given, is this significantly different from the othervalues calculated? Consider a confidence level of 95%.

22.3 Supposing that two chemists A and B, whose results figured in question 21.1above, used two different apparatus. In order to determine if the precisionof these apparatus is significantly different apply a test of variance, F .

where � F = s2A/s2

B

PROBLEMS 517

22.4 Once again return to the results of 21.1, and chemists A and C in particular.If the true value is 131�9 g/L calculate and compare the respective valuesof parameter t for these chemists. Can the presence of a systematic errorbe concluded for the data of either A or C?

22.5 The results of experimental measurements repeated four times were thefollowing: 24.24, 24.36, 24.87, 24.20, 24.10. Verify whether the third value,which seems to be high compared to the others, should be considered as avalue out of acceptable range.

Consider now two complementary measurements: 24.12 and 24.25.Consider again the question posed above and conclude by applying thecalculation of the standard deviation, s

22.6 The measurements were recorded and then repeated six times for twodifferent methods, for each giving: average 42 (s = 0�3), and average45(s = 0�2).

— Do these two methods yield results that are significantly different?

22.7 A compound is accompanied by a certificate indicating its purity as being99% with s = 0�08, established over five analyses. Four control measure-ments performed upon the same compound led to the following values:98.58, 98.62, 98.80 and 98.91. Should the original value be rejected?

22.8 A series of standards used in atomic absorption led to the following results:

Concentration g/L 1 2�5 5 10 20 30Absorbance 0�06 0�19 0�36 0�68 1�21 1�58

— Might the method of linear calibration graph be used with these resultsand, if so, over which range of concentrations?

22.9 A series of measurements must be repeated five times. Eight successivevalues for the blank used in the analysis yielded the following: 0.3, −0�75,−0�3, 1.5, −0�9, 1.8, 0.6 and 1.2.

— Calculate the limit of detection by applying a 99% confidence level.

Solutions

1 Chromatography, general aspects

1.1 At equilibrium the 40 mL of eluant contains 12 × 40/10 = 48mg ofcompound. There are therefore 100 − 48 = 52mg in the stationary phase.If K represents the ratio of the masses present in 1 mL of each phase inequilibrium, then K = �52/6�/�48/40� = 7�2.

1.2 When a molecule of the compound migrates along the column it passesalternately from the mobile phase, where it progresses at the speed of thisphase, to the stationary phase where it becomes immobilised. The averagevelocity for the passage is then reduced in relation to the amount of timespent by the molecule in the stationary phase, increasing by consequencethe value for tS.

Now consider the total mass, mT, of all of the identical molecules inthe sample. Statistically at each moment, there will be a certain numberof these molecules within the stationary phase while the rest remain in themobile phase. The ratio of these molecules fixed in the stationary phase(mS), and of those present in the mobile phase (mM), will be the same asthe ratio representing the sum of the intervals spent in each phase for asingle isolated molecule; that is: mS/mM = tS/tM.

Thus k will correspond to the ratio tS/tM and since tS = tR − tM then wecan refind the classic expression for the retention factor (or capacity factor),as calculated from the chromatogram:

k = �tR = tM�/tM

1.3 The separation factor (or selectivity factor), is generally calculated from theretention time tR, yet in the question it is the retention volumes VR whichare given for the two compounds. However, VR and tR are linked by anexpression which considers the flow of the mobile phase, D:

VR = D · tR


520 SOLUTIONS

Therefore if for the expression in � below, each tR (or tM) is replaced byVR (or VM), we will have:

� = �tR�2� − tM�/�tR�1� − tM� = �VR�2� − VM�/�VR�1� − VM��

which leads to � = 1�2.

Note: The expression in � is defined from the retention volumes and remainsuseful with a flow gradient but it is very rare that it is employed since theapparatus does not measure the instantaneous rate of the column. Thereforethe calculation of the retention volumes (other than by substituting in therelation, VR = D · tR) is not permissible.

1.4 The expression giving the retention factor can be written, tR = tM�1 + k�,where tM corresponds to the ratio between the length L of a column andthe average velocity u of its mobile phase. Equally, k = KVS/VM, leadingupon substitution to

tR = �L/u��1 + KVS/VM��

1.5 In order to incorporate k into expression 1, the relation tM = tR/�1 + k�, isused. Expression 1 then becomes:

Neff = 5�54

(tR − tR

1 + k

)2

w21/2

simplifying to

Neff = 5�54 × t2R

(1 − 1

1 + k

)2

w21/2

and then Neff = Nk2

�1 + k�2

1.6 The classic formula giving the resolution implies that the peaks are Gaussian.The known relationship between w�w1/2 and � permits the replacement ofw by 4 · w1/2/2�35.

1. The basic formula then becomes,

R = 2tR�2� − tR�1�

4�w1/2�1/2�35 + 4�w1/2�2/2�35= 1�18

tR�2� − tR�1�

�w1/2�1 + �w1/2�2

SOLUTIONS 521

The formula, proposed in the question, leads to an error of approximately20%.

2. If these peaks are adjacent then the widths of their bases will generallybe comparable. Allowing therefore w = w1 = w2 and expressing w as afunction of N2 we will have:

R = tR�2� − tR�1�

w2

with1

w2

= 1

4

√N 2

1

tR�2�

leading, on combination, to:

R = 1

4

√N2

tR�2� − tR�1�

tR�2�

k can then be introduced by incorporating the general expression, tR =tM�1 + k�,

R = 1

4

√N2

k2 − k1

1 + k2

then, finally by introducing � = k2/k1:

R = 1

4

√N2

k2 − k2/�

1 + k2

leading to1

4

√N2

k2

1 + k2

� − 1

�

1.7 1. In the basic relationship

R = 2tR�2� − tR�1�

w1 + w2

we can replace w by expressing it as a function of N , w = 4tR√N

which

will give

w1 + w2 = 4√N

�tR�1� + tR�2��

and then,

R = 1

2

√N

tR�2� − tR�1�

tR�2� + tR�1�

since tR = tM�1 + k�, substitution of this relation leads to,

R = 1

2

√N

k2 − k1

2 + k1 + k2

522 SOLUTIONS

2. In multiplying the second term in the equation above by k2 + k1/k2 + k1

we can write the following intermediate relation:

R = 1

2

√N

k2 − k1

k2 + k1

k

k + 1

Then by introducing � and substituting, we arrive at expression 2.

1.8 In supposing that the following equation is true:

R = 1

4

√N

k

1 + k

� − 1

�

then,

N = 16R2( �

� − 1

)2(

k + 1

k

)2

but Neff = N

(k

1 + k

)2

which on substitution will lead to the expression given in the question.

1.9 R1 = �0�5 × 60�/�10 + 12� = 1�36; R2 = 1�47, (k2 = 9�5, � = 1�056 and N2 =15 270) R3 = 1�5�k1 = 9�; R4 = 1�5.

1.10 1. The viscosity of the stationary phase increases with tempera-ture as experienced when a pre-programmed rise in tempera-ture induces a loss of charge across the column. As a resultthe gas flow vector measured, before the analysis is begun, willbe reduced. The average velocity of the gas vector is likely tobe different from its optimal value, with an increase in pressurenecessary which requires that the chromatograph possesses a flowcontrol.

2. The Van Deemter equation of type H = f �u�, has the derivatived�H�/d�u� = −B/u2 + C. This expression cancels to zero when u =�B/C�1/2. The value reported in the Van Deemter expression leads toH = A + 2�BC�1/2. This calculation becomes important if several experi-mental points (Hi�ui) are employed to find the coefficients A, B and Cof the equation.

1.11 The solution of this problem returns us to the initial three lines of exercise1.7, where we considered employing the retention volumes in place of theretention times.

SOLUTIONS 523

1.12 1. Flow of the mobile phase, k, column temperature.

2. Yes.

3. Yes.

2 Gas chromatography

2.1Speed of

separationInjectioncapacity

Retentionfactor k

Selectivityfactor �

Effectiveness

Increase incolumn length

− 0 0 0 +

Increase incolumn diam.

0 + − 0 0

Increase in filmthickness

− + + 0 +

2.2 1. Neff , k, �.

2. GC: methane. HPLC: uracil, D2O� � �

3. Following the experiment three equations can be proposed for the threeunknowns: tM, a and b.

log�271 − tM� = 6a + b (1)

log�311 − tM� = 7a + b (2)

log�399 − tM� = 8a + b (3)

— in multiplying (2) by −1 and adding to (1):

log�271 − tM�/�311 − tM� = −a (4)

— in subtracting (2) from (3):

log�399 − tM�/�311 − tM� = a (5)

The resolution of these simultaneous equations yields, tM = 237�7 s.

4. The Kovats graph passes through the points C7 and C8.

log�399 − 237�7� = 2�207 and log�311 − 237�7� = 1�863

log�246 − 237�7� = 2�033

524 SOLUTIONS

thus �2�033 − 1�863�/x = �2�207 − 1�863�/1; so, x = 0�494, therefore Ik =700+49=749. The McReynolds constant of the pyridine on this stationaryphase is 749 − 695 = 54.

2.3 K = k� and � = Di/4ef therefore ef = k · Di/4 · K. Since Di = 200�m, k =�200 − 40�/40 = 4, and K = 250, leading to ef = 0�8�m.

2.4 The volume V leaving a capillary column per second is equal to the internalvolume of the column multiplied by the length u. The internal section of thecolumn is given by: D2

i /4,

V = u D2i /4

The flow in mL/min (if u and Di are in cm) is given by D = 60V.If it is chosen to express Di in mm, this being a value 10 times larger than

that given in cm, we must introduce a factor of 0.1 and the expression wouldthen become: D = 60u D2

i 0�01/4, leading to D = 0�47uD2i .

2.5 1. We note that the elution order follows accurately the points of the graph.Since the alkenes are more polar than the corresponding alkanes theymigrate faster, as would be expected upon a non-polar column.

2. The selectivity factor is known, � = k2/k1 and therefore the followingvalues are found for the temperatures indicated: 1.12 (at −35 �C), 1.11 (at25 �C), and 1.09 (at 40 �C).

3. Although the column remains the same, the retention times will bedecreased as a result of the parallel reduction in the coefficient K =CS/CM

with the temperature.

4. 138 489 theoretical plates are indicated from the application of the formularecalled from exercise 2.7.

5. Hmin = 0�113mm.

6. Coating efficiency: 52%.

7. From these three expressions:

ln 0�408 = a/238 + b

ln 0�148 = a/298 + b

ln 0�117 = a/313 + b

we find that a = 0�00814 and b = 0�00493.

SOLUTIONS 525

2.6 Knowing that the retention time for butanol is reduced we can calculatethe number of equivalent carbons in an alkane which would have the sameretention time. We find 6.45. The Kovats factor of the butanol is therefore645. The corresponding McReynold’s constant will be

645 − 590 = 55

2.7 1. Knowing the retention time and the capacity factor of the secondcompound we can use the relation, tR = tM�1+k� to calculate the hold-uptime, finding: tM = 50 s.

2. The formula proposed enables the effectiveness of the column N2 to becalculated for the second compound, which is: N2 =22 861. Subsequently,knowing equally that:

N2 = 5�54t2R/w2

1/2

it is easy to isolate w1/2, and to calculate its value: 4.67 s. Bearing in mindthe scale of the chromatogram, this time interval corresponds to:

�4�67/60� × 10 = 0�77 mm�

3 High performance liquid chromatography

3.1 1. The flow of the mobile phase in a column is proportional to its cross-section and to the linear velocity of progression for identical contents(D= s ·v). The cross-section equally varies with the square of the diameter(s = k · d2). Thus,

v2/v1 = k d21D2/k d2

2D1

v2/v1 = �1/0�004� × �0�3/4�6�2 = 1�06

2. The hold-up volume is VM = tMD = 4 × 4 = 16�L.

3. For the final peak: tR = 48 min, thus VR = 48 × 4 = 192�L or 0.192 mL(around 4 drops!). The first advantage of a narrow column is its economyin the use of solvent.

4. The efficiency of the column, as calculated by the classical formula, gives67034 plates.

5. k = �48 − 4�/4 = 11.

6. The stationary phase is of a functionalised silica-type, as indicated bydifferent annotations on the base of the chromatogram.

526 SOLUTIONS

7. The hold-up volumes are in the same ratio as the two cross-sections ofthe columns

v0�3/v4�6 = �0�3/4�6�2 = 0�0043

Elsewhere the coefficient K (or the values of k) of the compounds doesnot change from one column to another, therefore the retention volumes,VR = VM�1 + k�, remain the same as the hold-up volumes. The retentionvolume of the narrow column (0.3 mm) is therefore equal to that of thebroader column �4�6mm� × 0�0043 (a factor of 235 times less).

8. Since the volume injected was the same, it will be 235 times more concen-trated in the mobile phase of the narrow column and therefore in theorythe signal should be 235 times more intense at the maximum of the peak.

The second advantage of narrow columns is that, for detection, they aremore sensitive.

3.2 At pH 9, the acids are in the form of their corresponding carboxylate ions.These ions have the tendency to be strongly attracted by the polar aqueousphase. The hydrophobic part (the carbon chain), guards their contact withthe stationary phase. The polarity of this chain will decrease in the compoundorder 1, 3 and 2, which is the order of elution for the compounds.

3.3 1. c – Reverse phase

2. a – Gel permeation

3. d – Ionic chromatography

4. b – Normal phase

3.4 These compounds are very polar and are therefore little retained by a phaseof type RP-18. At pH 6, the ATP is the first to be eluted from the columnsince it is the most polar. ADP will follow and then finally AMP. If, however,an ammonium salt of type phase transfer is added to the mobile phase thendipole–dipole interactions will be created with the three nucleotides. Thecomplex made with the ATP is the strongest and is therefore retained thelongest, hence the order of elution is reversed.

3.5 1. If the selectivity factor � = 1, it must be that the peaks are superimposedand that the retention times are the same which implies that the respective

SOLUTIONS 527

retention factors k, and therefore log k, also have the same value. The %MeCN is then verified by solving the following expression:

−0�0107%MeCN + 1�5235 = −6�075 = − 6�075 × 10−3% MeCN

+ 1�3283

leading to MeCN = 42�2%.

2. The values of log k can be found from the equations given in the text:

Compound A� k30 = 14� k70 = 8

Compound B� k30 = 16� k70 = 6

It is now possible to calculate values of � for the two compositions. Whenusing 30% of MeCN: �=16/14=1�1428 while for 70% of MeCN: �=8/6=1�333.

In applying the formula yielding the resolution as a function of k and�: R = 1/4N 1/2�� − 1�/� · k/�k + 1�, we find that substituting the termsin � and k will yield 0.222 for 70% and 0.1176 for 30%. Therefore it ispreferable to utilize the MeCN in a proportion of 70%, which also conveysthe advantage of leading to a more rapid separation.

4 Ion chromatography

4.1 The stationary phase is of a cationic type. In the dry state it remains in anon-dissociated form but when water is added and in the presence of a highconcentration of sodium ions, the following equilibrium is attained in whichthere is a liberation of H+:

RSO3H + Na+�R − SO3Na + H+

The calculation of the molar capacity of the stationary phase is as follows:

25�5 × 0�105/1000 = 2�6775 × 10−3 mol/g

The equilibrium above is long in establishing itself such that the additionof the sodium hydroxide solution removes all of the protons liberated. Acertain time is required for them to reappear in solution.

Note: The helianthin �Me�2N�C6H4�N = N�C6H4� − SO3Na is another namefor methyl orange, which colours red for pH < 3�2 and yellow for pH >4�4��max = 505nm�.

528 SOLUTIONS

4.2 1. Such a phase corresponds to a polymer (250000 < M < 900000)comprising acid groups, −CH2COOH, and is therefore weakly cationic.The pH of the separation is inferior to the pI of proteins, thus their aminofunctionality will be fully protonated �−NH+

3 �.

2. If the pH is increased then the ionic character of the column is reducedleading to a faster elution of the proteins. Here pI1 < pI2 < pI3.

4.3 1. The concentration factor is 5 at the beginning since we have 1 mL of plasmaand, following treatment of this extract, there will be 200�L remainingof the solution containing the same amount of cyclosporin as the 1 ml atthe beginning.

2. No, because we cannot weigh the collected cyclosporins A or D.

3. a) Method of internal standard.Following convention we will give the letter A to cyclosporin A and D to

cyclosporine D as used in the internal standard:

kA/D = mAAD/mDAA = CAAD/CDAA

To calculate the relative response coefficient we will take for example thesolution containing 400 ng/ml of cyclosporin A:

kA/D = �400/250� × �1/2�04� = 0�784

C ′A = C ′

DkA/DA′A/A′

D

The chromatogram of the sample for which A′A/A′

D = 9/14 (heights of thepeaks measured from the original chromatogram), leads to

C ′A = 250 × 0�784 × 9/14 = 126ng/mL

b) Method of calibration curve. Plot the graph of the ratios of the peak heightsagainst concentration C of cyclosporine A.

By the method of least squares we find:

Rh = 0�005092C − 0�00411

For Rh = 9/14�C = 127�1ng/mL.

Note: If we evaluate Rh incorrectly then we commit an error of some impor-tance which is of course translated into the result. However, frequently, forvery weak concentrations, we can estimate with respect to a limit below

SOLUTIONS 529

which the error holds less importance, e.g. in taking Rh = 8/15 rather than9/14, the difference will be 20% and we will find that C = 104ng/mL.

4.4 Through the application of the general expression we will have a total offour formulae giving the % mass of the various esters. Below is an examplefor the methyl butanoate ester:

%ME = 100AME × 0�919

AME × 0�919 + AEE × 0�913 + APE × 1�06 + ABE

We will solve this by taking and substituting the areas given in the question:

%ME = 16�6

%EE = 16�6

%PE = 33�4

%BE = 33�4

Note: The scale in mV corresponds to UV detection.

4.5 1. The addition of N-methylserotonin before the extraction is made removesthe necessity of counting any eventual loss of product due to the differentintermediate manipulations. We can suppose that the yield of the extrac-tion is the same for the two compounds, which are structurally verysimilar.

2. To determine the relative response factor kS/NMS of the serotonin (S), withrespect to its N-methyl derivative (NMS), the following relation is used:

kS/NMS = mS

mNMS

× ANMS

AS

= 5

5× 30956727

30885982= 1�002

3. Measuring the sample:

mS = mNMSkS/NMS

A′NMS

A′S

= 30 × 1�0022573822

17 19818= 45ng/mL

which gives a concentration of approximately 45 ppb, for an aqueoussolution.

530 SOLUTIONS

5 Thin layer chromatography

5.1 1. RF�A� = 27/60 = 0�45�RF�B� = 33/60 = 0�55

NA = 16 × 272/22 = 2916�NB = 16 × 332/2�52 = 2788

HA = xA/NA = 9�26 × 10−4 cm�HB = xB/NB = 1�18 × 10−3 cm

2. R = 2�33 − 27�/�2 + 2�5� = 2�67

3. From the definition for the selectivity factor and from the relation linkingRF and k, we arrive at:

� = �RF�B�/RF�A�� · �1 − RF�A��/�1 − RF�B�� = 1�49

5.2 1. Since it arises from a normal phase, the more polar compound will beretained the longest. In order of increasing migration distances we willhave C, then B and finally A.

2. The order of elution will be A, B then C, reflecting the migration times.

3. Reverse order.

4. Approximate value for RF�A� = 22�5/50 = 0�45. HETP = L/N with N =5�54x2/d2 = 5�54 × 22�52/22 = 701, leading to HETP= 50/701= 0�07 mm.

7 Size exclusion chromatography

7.1 In size exclusion chromatography K < or = 1, excepting cases where interac-tions develop between the solute and stationary phase since this creates a parti-tion phenomenon which superimposes itself upon the diffusion in the pores.

7.2 By placing the following two columns end to end, first column C will separatethe masses of 3 × 106 and 1�1 × 106 Da from the remaining two. These twomasses will subsequently be separated by the column A. On the correspondingchromatogram we will obtain four distinct peaks.

7.3 1. See graph.

2. The total exclusion or interstitial volume is approximately 4.2 mL. Theintraparticle volume of the pore is close to: 7�9 − 4�4 = 3�5ml.

3. For the mass of 3 250 Da, K = �5�4 − 4�4�/�7�9 − 4�4� = 0�29

SOLUTIONS 531

8 Capillary electrophoresis and electrochromatography

8.1 1. Since it is known that �app = �EP + �EOS therefore �EP = �app − �EOS andsince the experiment allows access to the velocities: �app and �EOS. Thenby substitution

vapp = 24�5/�60 × 2�5� = 0�163 cm/s

and

vEOS = 24�5/�60 × 3� = 0�136 cm/s�

As a result: vEP = 0�163 − 0�136 = 0�027 cm/s.

�EP = vEP/E = 0�027 × 32/30000 = 2�88 × 10−5cm2 s−1 V−1�

2. D = l2/�2Ntm� = 24�52/�2 × 80000 × 150� = 2�5 × 10−5 cm2 s−1.

8.2 1. See the scheme in the book.

2. No, since it arises from a non-treated internal surface, which at the pHconsidered acts as a polyanion. This results in the creation of an electro-osmotic flow. The fact that the compound migrates towards the cathodedoes not necessarily mean that it is carrying a net positive charge. Thepossibility remains that it is being trained in that direction, even if carryinga negative charge. Following convention:

3. l = �appt and �app = �app/E = �appL/V therefore �app = lL/Vt.

�app = 7�5 × 10−4 cm2 s−1 v−1

4. Following the same reasoning, this leads to �EOS = lL/Vtm.

�EOS = 1�5 × 10−3 cm2 s−1 v−1

5. �EP = �app − �EOS thus �EP = −7�5 × 10−4 cm2 s−1 v−1

6. The negative character of �app implies that it originates from a speciescarrying a net negative charge. The compound will migrate more slowlythan a neutral marker.

7. If the internal lining is rendered neutral there would be no more electro-osmotic flux and as a result the compound will no longer migrate towardsthe cathode but will reappear in the anode compartment.

532 SOLUTIONS

8. If the pI is 4 for all pH less than 4, then the compound will be in theform of a cation. In this case, the migration time will normally be shorterthan for a neutral marker.

9. In using the formula recalled in the question, we will find 337 500 theo-retical plates.

10. A small molecule diffuses faster than a larger one. Therefore the effec-tiveness is greater for molecules of greater mass.

8.3 The two control compounds enable the following simultaneous equations tobe written:

log 45000 = 1�5a + b (1)

log 17 200 = 5�5a + b (2)

The resolution of these two equations lead to a=−0�1 and b=4�8. Therefore,log M = −0�1� + 4�8 and by substituting � = 3�25 we find

log M = 4�48 and so M = 29854Da�

Note that the stationary phase does not behave like an SEC gel since it createsobstacles for the larger molecules which are forced to migrate more slowlythan their smaller counterparts.

8.4 If the isoelectric pH of B is superior to that of A then this is because the pHat B oversteps with respect to the position of A. Therefore the pH increasesfrom the right to the left of the capillary.

If B is displaced further towards the right it will become positively chargedand will therefore migrate towards the left and its original position whichis stable. The positive pole is therefore to the right and the negative one tothe left. The electric field therefore applies itself from right to left on thecorresponding diagrams.

8.5Protein pI pH = 3 pH = 7.4 pH = 10

Insulin 5�4 + − −Pepsin 1 − − −Cytochrome C 10 + + 0Haemoglobin 7�1 + − −Albumin serum 4�8 + − −

SOLUTIONS 533

9 Ultraviolet and visible absorption spectroscopy

9.1 The application of the expression E =h�� for one mole is written E =N�h��=N�h�c/� leading to:

E = 6�022 × 1023 × 6�6262 × 10−34 × 3 × 108/�300 × 10−9�

= 399030 J� 399kJ or� 399/4�18 = 95�5kcal�

9.2 A = ��l�C = 650 × 7 × 10−4 × 2 = 0�91. If the optical path length is doubledthe absorbance will equally be doubled: A = 2 × 0�91 = 1�82.

9.3 1. If T = 0�5�A = log 1/0�5 = 0�3.Since, A = ��l�C�� = 0�3/1�28 × 10−4 = 2344 l mol−1 cm−1.

2. If the concentration is doubled, A = 0�6, therefore log 1/T = 0�6 thusT = 0�25 and the percentage transmittance is 25%.

9.4 The concentration of a solution of 0.1 ppm is 0�1 × 10−3 g/L. The molarconcentration is therefore 0�1 × 10−3/52 = 1�92 × 10−6 mol/L. We can thuscalculate:

l = A/��C� = 0�4/�41700 × 1�92 × 10−6� = 4�98 cm

Therefore a cell of 5 cm pathlength is well adapted.

9.5 If 90% of the radiation is absorbed, T = 0�1. Thus A = 1 and C = 1/�0�03 ×15000�=2�22× 10−3 mol/L. For M =500g/mol, we find, that m=1�11g/L.

9.6 1. 207 + 12 = 219nm �exp�max = 218 in EtOH);

2. 215 + 12 + 12 = 239nm.

3. 215 + 60 + 5 + 12 + 18 + 39 = 349nm (exp�max = 348 in EtOH);

4. 215 + 5 + 10 + 12 = 242nm.

534 SOLUTIONS

9.7 To resolve this problem we use the fact that absorbances are additive:

AT = CA�l��A + CB�l��B

From these two reference solutions we can calculate �A and �B at 510 nm:

�A = AA/�CA�l� = 0�714/�1�5 × 10−1� = 4�760

�B = AB/�CB�l� = 0�298/�6 × 10−2� = 4�967

and calculate the same for �′A and �′

B at 575 nm:

�′A = A′

A/�CA�l� = 0�097/�1�5 × 10−1� = 0�647

�′B = A′

B/�CB�l� = 0�757/�6 × 10−2� = 12�617

By virtue of the addition of absorbances we can now write for the mixture:

0�671 = 4�76CA + 4�967CB

0�330 = 0�647CA + 12�617CB

The resolution of this two equation system leads to:

CA = 1�2 × 10−1 mo1/L and CB = 2�0 × 10−2 mo1/L�

9.8 1. See graph.

2. The equation of the graph (absorbance against concentration) is:

A = 1�3771C + 0�0024 �R2 = 0�9987��

3. For an absorbance of 0.45, C = 0�325mol/L.

9.9 1. The equation of the calibration graph is: Y=0�232C+0�162 �R2 =0�9834�.

2. For a reading of Y = 3�67�C = 15mg/L in the sulphate ion.

10 Infrared spectroscopy

10.1 1. A wavenumber of 1000 cm−1 corresponds to a wavelength of 10�m asE = h� = hc/�. E = 6�62 × 10−34 × 3 × 108/�10 × 10−6� = 1�99 × 10−20 J.For one mole we would have 12 000 J (that is 2.87 kcal/mol).

SOLUTIONS 535

2. � = 1

15 × 10−4= 666�67 cm−1

3. The absorbance A is such that: A= log 1/T . If T =0�05�A= log 1/0�05=1�3.

10.2 We can accept that the force constant k remains the same for the two speciessince they are isotopes of the same element. Thus �H = �12 × 1�/�12 +1� amu and �D = �12 × 2�/�12 + 2� amu.

�H

�D

=√

�D

�H

We will find �D = 2215 cm−1 which represents a difference of less than 2%from the experimental value.

10.3 The approximate mass of the carbonyl group will be:

�CO = 12 × 16

12 + 161�66 × 10−27 = 1�138 × 10−26 kg�

then substituting,

k = 4 2�2c2�CO = 4 2 × 17102 × �3 × 1010�2 × 1�138 × 10−26 = 1183N/m

(Note the speed of light must be expressed in cm/s here).

10.4 A photon corresponding to 2000 cm−1 will transport an energy of

E = hc/� = 3�972 × 10−20 J�

This energy is transformed into mechanical energy: ETOT =EKIN +EPOT. Atthe maximum of the elongation �x, EKIN = 0 because the velocity is zero.The energy of the photon E is therefore entirely in the form of potentialenergy: �EPOT = 1/2k��x�2. �EPOT = E carried by the photon.

�x =√

2�E

k=√

2 × 3�972 × 10−20

1000= 8�91 × 10−12 m

which is about 6% of a bond whose length is 0.15 nm.

10.5 The two sets of vibrational frequencies have for their origin the two isotopesof chlorine in the sample of HCl (75% of 35Cl and 25% of 37Cl). When the

536 SOLUTIONS

same transition is considered for the two molecules, reunited in the sample,only the reduced mass differs, leading to the separation. The calculationleads to: ��35�Cl/��37�Cl = 0�9985.

�37

�35

= √0�9985 = 0�9992

Thus towards 3000 cm−1 the difference is 2�3 cm−1.

10.6 A similar calculation as exercise 10.3 leads to k = 1846N/m.

10.7 1. By linear regression we find: A/d = 0�0009x + 0�0003 �1�, where x is theVA% in film.

2. By the method of least squares we find: A1030/A720 =0�0531x+0�0047 �2�.

3. From equation (1), for the unknown film VA% = 8�44; from equation(2) VA% = 8�46.

10.8 1. From the application of the Felggett advantage: in calling S/N the signalto noise ratio:

S/N = 10 × �1/16�1/2 = 2�5

2. � = 2x therefore R = 1/2x and so x = 1/2R = 0�5 cm.

3. If � = 15800 cm−1, � = 0�633�m. In passing from one minimum to thenext the mirror must be displaced by a distance corresponding to ahalf-wave-length which is 0�316�m.

11 Fluorimetry and chemiluminescence

11.1 The wavenumber corresponding to a wavelength of 400 nm is25000 cm−1�1/400 × 10−7 = 25000�. The Raman peak is displaced towardslonger wavelengths and will be located at 25000− 2880= 22120 cm−1. Thisvalue corresponds to a wavelength of 452 nm (107/22120).

11.2 A wavelength of 250 nm corresponds to a wavenumber of 40000 cm−1.The Raman peak of water will therefore be situated at 40000 − 3380 =36620 cm−1, corresponding to a wavelength of 273.1 nm.

SOLUTIONS 537

11.3 1. The use of the same control source of fluorescence to compare themeasurements made under the same conditions leads to the followingsimple calculations: the concentration of the unknown sample solutionis �60/40� × 0�1 = 0�15ppm or 150 ppb.

2. We can calculate the difference in cm−1 between the light of the sourceand 456 nm (measurement), to see if the displacement is 3 380 cm−1.By the introduction of a fluorospectrometer we could equally judge, bystudying the spectra, the effects upon the fluorescence of a displacementof the wavelength of excitation of several nanometers.

11.4 1. The benzopyrene has a rigid polycondensed aromatic structure, typicalof fluorescent compounds. Forming part of the PAH, it is currentlymeasured by HPLC in drinking water by using a method of detection byfluorescence.

2. The fluorescences being additive, the analysis begins with the correctionof the values read for the three solutions by subtracting the value read forthe blank. These new values become 21, 35.1 and 29.8. To calculate theconcentration of the sample solution one can write: �1�25−0�75�/�35�1−21� = �x − 0�75�/�29�8 − 21�, finding x = 1�062�g/mL.

3. This value corresponds to the mass of benzopyrene which is found in 1litre of air (� = 1�3g/L). The mass concentration is therefore

1�06 × 10−6/1�3 = 0�815ppm or 815ppb�

11.5 The method followed is that of addition by measurement: we will resolvethis problem easily. In 1 mL of the solution of iron 5�15 × 10−5 M there are5�15 × 10−8 moles of Fe. We will therefore have

29�6/�5�15 × 10−8 + x� = 16�1/x�

which leads to x=6�142×10−8 moles for 2 mL. From this the concentrationof the solution of Fe II is 3�07 × 10−5 M.

11.6 1. Hydroxyquinoline and zinc form a chelate (one atom of the metalis inserted between two molecules of the complexant), which can beextracted with tetrachloromethane and which yields fluorescence. Thefour solutions treated being each in the same manner suggests that wemight suppose the yields of the extraction to be identical.

538 SOLUTIONS

2. By application of the least squares calculation the following equation canbe derived:

If = 1�5V + 7�74 �VmL�

3. For an intensity of fluorescence If =0, we will find V =5�16mL. In 1 litreof the solution B there is 0.0136 g of zinc chloride, which is 6�538�g/mLof Zn. Therefore 5 mL of unknown solution contains 6�538 × 5�16 =33�736�g of Zn. Per litre there will be 200 times more, i.e. 6747�2�g,representing a concentration of 6.75 ppm.

11.7 1. The five standards (1 to 5) correspond to the following concentrationsC (in g/L), �1� = 0�0001; �2� = 0�00008; �3� = 0�00006; �4� = 0�00004;�5�=0�00002. With these values derived from the method of least squaresthe equation of the graph is:

If = 1773285C + 2�22

2. The sample of drink whose fluorescence is 113 following a dilution bya factor of 1 000 corresponds to a calculated concentration of 6�25 ×10−5 g/L. The drink, non-diluted, yields a concentration of 6�25 ×10−2 g/L which is approximately 62.5 ppm.

3. When we follow a protocol we make measurements of fluores-cence at a fixed wavelength which renders the trace of the spectrumredundant.

12 X-ray fluorescence spectrometry

12.1 1. The solution is an equilibrated mixture of the elements constituting thesample. In 8 g of KI (166 g/mole), there are:

8 × 39/166 = 1�98g of potassium and 8 × 127/166 = 6�12g of iodine.

In 92 g water (18 g/mole), there are:

92 × 2/18 = 10�22g of hydrogen and 92 × 16/18 = 81�78g of oxygen.

The balance of the mixture by gram is:

�m = �1�98 × 16�2 + 6�12 × 36�3 + 1�2 × 81�78 + 10�22 × 0�4�/100

= 3�56 cm2/g�

SOLUTIONS 539

2. �=3�56×1�05=3�738 cm−1 since P =P0 exp−�x, thus finding P/P0 =0�024 which is 2.4%.

12.2 E = h�c/� therefore � = h�c/E

�nm = 109 × �6�626 × 10−34 × 2�998 × 108�/�EeV × 1�602 × 10−19�

= 1240/EeV

�Å = 1240 × 10/�EkeV × 1000� = 12�4/EkeV

12.3 1. 2d sin � = k�� (here k = 1)

sin � = 8�126/�2 × 4�404� = 0�9226 therefore � = 67�31 �

The deviation 2� = 134�62 �.

2. E = h�c/� substituting �6�626 × 10−34 × 3 × 108�/�0�209 × 10−10� =9�517 × 10−15 J or 59 480 eV.

12.4 1. The crystal sweeps through the angle � between two extreme values.By the application of 2d sin � = k��, if � = 10 �� = 0�047 nm and if� = 75 �� = 0�262nm.

2. The formula for the conversion �Å = 12�4/EkeV leads, for the two wave-lengths above, to E = 26�38keV and E = 4�73keV, respectively.

12.5 1. �E/E = ��/�, therefore �E = E��/� = �h�c/��/�� =�h�c/�2�� E = 1�9284 × 10−19 J or 1�9284 × 10−19/�1�6 × 10−19� =1�2 eV.

2. We will not be able to distinguish these two transitions arising from thesulphur atom.

3. A variation of 2 × 10−4 nm corresponds to a difference in energy of lessthan 1 eV, which will be invisible on the spectrum.

12.6 The table of mass attenuation coefficients indicates that for aluminium andthe K� of copper, �m = 264 cm2/g. Knowing the density of this metal leadsus to the linear coefficient:

� = 264 × 2�66 = 702 cm−1�

540 SOLUTIONS

The fraction transmitted: P/P0 = e−702×12�10−4 = 0�43. By consequence 57%of the radiation is absorbed by the aluminium film.

For the emission K� of silver, �m = 2�54 cm2/g. By application of thesame calculations we will find that P/P0 = 0�99. In this case only 1% of thismore energetic radiation will be absorbed.

In initial calculation of the coefficient for the latex �M = 68g/mole�, weare aided by the values given in the question:

�m = �60 × 25�6 + 8 × 0�43�/68 = 22�64 cm2/g�

The same sequence of calculations will lead to P/P0 = 0�89.

12.7 1. At least one electron is required in the shell ‘L’ e.g. n = 2.

2. This is because the constituents of air absorb weakly energetic radiationof fluorescence X. The helium is almost completely transparent.

12.8 For the X-ray beam to reach the detector with sufficient intensity theincident radiation will be required to hit the crystal over a surface largeenough such that thousands of atoms reflect the light in an identical fashion.If the angle of refraction is different from the angle of incidence thensuccessive atoms from the same horizontal reticular plane will return theradiation with an optical displacement which will appear as interference.

To avoid this we observe the reflection through an angle equal to theangle of incidence. The differences of pathway only cause interference dueto successive horizontal reticular planes.

12.9 We begin by establishing the ratio Mn/Ba for the two solid standard solu-tions. Therefore sol 1 = 0�813 and sol 2 = 0�9625 we can write:

�x − 0�25�/�0�886 − 0�811� = �0�35 − 0�25�/�0�9625 − 0�811�

leading to: x = 0�30%.

12.10 The coefficient of mass attenuation for water for the emission k� of Ni is:

�m = �16 × 13�8 + 2 × 0�43�/18 = 12�31 cm2/g�

Since � = 1�� = 12�31 cm−1. We will find that P/P0 = e−12�31 = 4�5 × 10−6.Therefore 1 cm of water is sufficient to stop almost all radiation of thisparticular strength.

SOLUTIONS 541

12.11 The mass attenuation coefficient of air for a radiation whose energy is 2keVis �m = �0�8 × 494 + 0�2 × 706�= 536�4 cm2/g. Since �= 0�0013g/mL��=0�697 cm−1 and P/P0 = 0�03. Attenuation attains 97%.

13 Atomic absorption and flame emission spectroscopy

13.1 For a given temperature, R=Ne/No =� · exp−�E/kT. By combining thisequation for the tube values of R such that R2/R1 the ratio of the two valuesof R to 2 000 K and 2 500 K leads to

R2

R1

= exp

[�E

K

(1

T1

− 1

T2

)]

For the resonance emission of sodium the value of �E = h�c/� is

�E = 3�37 × 10−19 J �or 2�1 eV��

Knowing that k = 1�38 × 10−23 J K−1�R2/R1 = 11�5. The measurement willtherefore be almost 12 times more sensitive at 2500 than at 2000 K.

13.2 EDTA yields complexes with a ratio of 1:1 with many metals. Better knownamong these complexes are those of bivalent cations which lead to hexa-coordinated ligands bound through the four acid functions and the twonitrogen atoms. The chelated ions pass more easily to the atomic state inthe flame since their volatility is increased.

13.3 Only a small proportion of sodium atoms are excited to the atomic state inthe flame, which leads to an underestimate of the quantity of this elementin a sample. If one adds potassium salt in a sufficient quantity with respectto the atoms of sodium, then a large number of potassium atoms will bepresent in the flame. These atoms lead to an oxydo-reduction reaction,

Na+ + K −→ Na + K+

In fact, according to the two ionisation potentials given, less energy isrequired to remove the least held electron within the potassium atom thanfor the corresponding electron of sodium.

13.4 The quantity of potassium ions introduced and expressed in moles is:

0�2 × 10 × 10−6 = 2 × 10−6 mole

542 SOLUTIONS

If the total volume of the solution has not changed and we call x thenumber of moles of potassium in the sample: 32�1/x = 58�6/�x + 2 × 10−6�from where it can be deduced that x = 2�42 × 10−6 mole. This quantity ispresent in 0.5 mL of serum, which is:

2�42 × 10−6 × 1000/0�5 = 4�84 × 10−3 mol/L�

13.5 If we call the signal of absorbance of the sample extracted from paprika Ax

and the sample solution AR�mX and mR are the corresponding masses oflead and we will have:

AX/AR = mX/mR therefore mX = mRAX/AR

AX = 1220�AR = 1000� mR = 10 × 0�01/1000 = 1 × 10−4 g

The sample introduced into the graphite furnace contains:

mX = 1 × 10−4 × 1220/1000 = 1�22 × 10−4 g�

The % mass is therefore 1�22 × 10−4/10−2 = 1�22%.

13.6 Calcium chloride dihydrate has a molar mass of 147.1 g. The concentrationof the parent solution is 1�834/147�1 = 0�01247 mol/L. Solution diluted 10:1�247 × 10−3 mol/L. The different solutions made up as standards have thefollowing molar concentrations in Ca++:

Standard 1/20: 0�623 × 10−4 mol/L signal 10.6Standard 1/10: 1�247 × 10−4 mol/L 20.1Standard 1/5: 2�494 × 10−4 mol/L 38.5Analytical blank: 0 mol/L 1.5

The equation of the calibration curve is: [signal] = 148900C + 1�407. Wewill find that the unknown solution is such that C =1�89×10−4. The parentsolution has a concentration 25 times greater, being 4�73 × 10−3 mol/L, or0.19 g/L in Ca++.

13.7 1. This parameter arises from the spectral band which is selected by the exitslit and will reach the detector. This is not the physical width of the exitslit which cannot be less than several micrometres.

2. EDTA has the molecular formula C10H16N2O8 while the mixed salt ofzinc and sodium is C10H12N2O8Na2Zn.

SOLUTIONS 543

The mass concentration of the parent solution is 35�7×10=357 mg/L.The diluted solution has the concentration C =2×357/100=7�14mg/L.The apparatus indicates that this solution corresponds to a concentrationof 0.99 mg/L in zinc. As a result the molar mass of the salt is 7�14 ×65�39/0�99 = 471�6g/mol.

The salt in the anhydrous state has a molar mass of 399.6 g/mol. Wecan therefore deduce that the difference �471�6−399�6�=72g representsthe mass of water, per mole, of this salt, which is 72/18 = 4moles. Weconclude therefore that the hydrate comprises four molecules of water.

3. A=0�321C +0�03, for A=0�369�C =1�14mg/L, a value too high, whichshows that for this measurement the calculation of least squares is notwell adapted.

4. The general answer to this question is no, since the experimental pointsare not aligned such that the range of concentrations extends more than1 mg/L. The apparatus proposes curves of preference.

14 Atomic emission spectroscopy

14.1 The elements which are measured are often in much smaller concentrationsthan all those constituting the matrix. Often it is necessary to identifycharacteristic emissions of trace elements (in concentrations of the order ofppm or less), mixed with elements which equally will yield emissions butwhose concentrations can only attain 10 or 20%.

We observe ionic emissions because the temperatures are very high andthe plasma is a medium rich in argon ions and in free electrons whichprovoke ionisation due to collisions with non-ionised atoms.

14.2 From E =h��, and if �E��t > h/2 then �� > 1/2 �t. Then � = c/�, so�� = �c/�2��.

Therefore,

�� ≥ 1

2 �t

�2

c

If � = 589nm and �t = 10−9 s, we will find �� > 1�84 × 10−13 m �1�84 ×10−4 nm�.Note: The imperfections of spectrometers and the Doppler and Stark effectscontribute to an important enlargement of the image of the entrance slit ofthe apparatus.

544 SOLUTIONS

14.3 From the data below we can construct the calibration graph of the ratio ofthe signal emission Pb/Mg against concentration.

Equation of the graph � ratio Pb/Mg = 8�219C + 0�345

For the two solutions � A = 0�118mg/L and B = 0�376mg/L�

14.4 The expression declares that the transition in energy which corresponds tothe emission of resonance is 16960 cm−1. This unit is employed to measurethe energies �E = h�c/�� with � = 1/� and � = 589�62nm. It is the firstcomponent of the doublet called the resonance line �E = 2�102 eV�. Thesecond is not a resonance emission.

14.5 Measuring radioactivity using a Geiger counter requires a sufficient numberof disintegrations to be accumulated in order to obtain a reliable result. If thehalf-life of the radionucleus is very long and the element not very abundantthen the rhythm of the decompositions will not be significant enough to bedistinguished from the background noise. An isolated counting can differenormously from the average since radioactivity results from a series ofrandom events which do not follow Gaussian behaviour.

Alternatively, the method of atomic emission works upon the total atomicpopulation of the isotope.

Example: 1 pCi/1 of 237Np (half-life 2�2 × 106 years) corresponds to apopulation of N = A/� = 3�7 × 1012 atoms, which can be represented as1�5 × 10−9 g/L (or 1.5 ppt).

Such a concentration is at the limit of the method based upon countingyet nonetheless is reliable for atomic emission spectroscopy (AES).

14.6 The linear dispersion represents the distance which separates, in mm, twowavelengths which differ by 1 nm. If the exit slit is 20�m�2 × 10−2 mm�,the bandwidth reaching the detector will be:

1 × �2 × 10−2�/2 = 1 × 10−2 nm�10pm��

15 Nuclear magnetic resonance spectroscopy

15.1 � =�Z/m with m=h/4 , thus � =4 �z/h=1�41. 10−26 ×4× /�6�6262×10−34�. � = 2�674 × 108 rad T−1 s−1

SOLUTIONS 545

15.2 The ratio of the populations is: NE�1�/NE�2� = e�E/KT with �E = �hB0/2 from the calculation 1.0000095. If Bo = 7 T, this ratio becomes 1.0000477.

15.3 1. If on the scale 4 cm represents 200 Hz (then 40 mm = 200 Hz), 7 H willcorrespond to

7/200 × 40 = 1�4mm�

2. If the apparatus operate at 200 MHz for 1H, it is nC =nH ·�C/�H for 13C.�C = 200 × 1/3�98 = 50MHz and 7 Hz will now correspond to �7/50� ×40 = 5�6mm.

15.4 1. The frequency of the apparatus is

2�6752 × 108 × 1�879/�2 × 3�1416� = 80MHz

The chemical shift is therefore: 220/80 = 2�75ppm.

2. The shift in Hz will be: 90 × 200/60 = 300Hz.

3. The chemical shifts do not change when they are expressed in ppm.

15.5 The proton spectrum of A presents a doublet of doublets. Two differentvalues for the coupling constants can be noted; one large, the other small�A = 2�.

The proton spectrum of B presents a triplet, therefore the proton is locatedat the same distance from two atoms of fluorine since the value of the couplingconstant is weak and can be considered to originate from compound 3 �B=3�.

The third isomer gives a triplet whose coupling constant will be of theorder of the distance separating the doublets of B, 1�2 × 60 = 72Hz. Thestructure corresponding to this spectral description is isomer 1.

1 � CHF2CCl3 2 � CHFClCFCl2 3 � CHCl2CF2Cl

15.6 When the nucleus of spin I = 1/2 is introduced into the magnetic field Bo,it self-projects into an orientation which follows the rule, m = (

12

)/(

h2 ).

Knowing the value for the spin vector we can write:

�√

3/2��h/2 � cos� = 1/2�h/2 �

which is

cos� = 1/√

3 or � = 54�7 �

546 SOLUTIONS

15.7 In NMR the intensity of the signals reflects the molar concentrations.Vanillin has a molar mass of 152 g, thus for 25 mg of this compound:

25 × 10−3/152 = 1�645 × 10−4 mole

Since 1 proton of the vanillin corresponds to a value of integration whichis half as strong as that of the proton of the unknown compound, wecan deduce that the number of moles of the latter is twice as great, being1�645 × 10−4 × 2 = 3�29 × 10−4 mole in 0.1 g of sample. The molar mass ofthe compound is therefore 0�1/�3�29 × 10−4� = 304g/mol.

15.8 From the gyromagnetic ratio we are able to calculate that the resonancefrequency of the chlorine is 188.255 MHz. Therefore between the two nucleiithere are 200 − 188�255 = 11�745MHz.

As 20 cm=10× 200Hz =2000Hz and 1 cm corresponds to 100 Hz, thenthe distance between the signals will be: 11�745 × 106/100 = 117 450 cm or1174.5 m!

15.9 Due to the reduction not going to completion the reaction mixturecomprises both acetone and isopropanol. 1 proton of acetone correspondsto 24/6 while a proton of isopropanol is 8/1 = 8. The yield will be R =100 × 8/�4 × 8� = 66�7%.

15.10 All of the compounds present in the mixture are submitted to the sameconditions. The spectrum recorded corresponds to a superimposition of thespectra of the individual constituents (the dilution of the sample in a solventdoes not modify its initial composition). Each constituent leads to either asingle or several signals: at 1.6 and 3.3 ppm for C2H5I, at 5.2 ppm for CH2Cl2and at 7–7.5 ppm for C6H5Br. To find the composition of the mixturewe will follow a reasoning close to that used in internal normalisation.An important difference concerns the relative response factors which canbe established without undertaking an analysis of a standard reference. Amolecule of dichloromethane (2H) will give a response which will be 2/5that of a molecule of bromobenzene (5H), or iodoethane (5H). If we dividethe respective areas indicated for each (84, 22.5, 31.5) by the correspondingnumber of protons (5, 2, 5), we will have the value (16.8, 11.25, 6.3) whichwill be proportional to the molar concentrations. Then, knowing the molarmasses of the three constituents (156, 84 and 157 g/mol), we can establishthe % mass with the aid of three similar formulas, as follows: take forexample CH2Cl2:

SOLUTIONS 547

%CH2Cl = 100 �area CH2Cl2/2� × 84/�area CH2Cl2/2� × 84

+ �area C2H5I/5� × 156 + �area C6H5Br/5� × 157

%C2H5I = 100× 16�8 × 156/�16�8 × 156� + �11�25 × 84�

+ �6�3 × 157� = 51%

%CH2Cl2 = 100× 11�25 × 84/�16�8 × 156� + �11�25 × 84�

+�6�3 × 157� = 18�4%

%C6H5Br = 100× 6�3 × 157/�16�8 × 156� + �11�25 × 84�

+ �6�3 × 157� = 30�6%

16 Mass spectrometry

16.1 If xn and xs are fractions of natural and synthetic vanillin, and �n =−20� �s =−30� �m =−23�5% the ratio of the isotopes of these two in natural, syntheticand a mixture of these variants, then:

xn + xs = 1

�nxn + �sxs = �m

then

xn = ��m − �s�/��n − �s�

Substituting, xn =6�5/10=0�65. The composition found is therefore 65%natural vanillin and 35% of the synthetic variant.

16.2 1. X = 2 × �174�97�/�389�42� = 0�899g of the element lutetium.

2. The extracted volume of 1 litre contains: �175�94�/�390�4� × 20 =9�013�g of 176Lu.

3. Coupled method ICP/MS.

4. The 175Lu is the only isotope whose mass spectrum displays a peak at175 mass units, while a peak at 176 could be due to either Yb or Hf.These elements constitute isotopic families. We could verify beforehandthe absence of peaks for the masses for Yb at 171, 172, 173 and 174, andfor Hf at 177, 178 and 179 mass units.

5. Let x be the mass (in �g) of Lu in the extraction of 11. This mass,before addition of 176Lu, comprises 0�974x of 175Lu and 0�026x of 176Lu.

548 SOLUTIONS

Following the addition of 176Lu the mass of 176Lu (in �g) is now0�026x + 9�013. Since the analysis indicates that the ratio of the intensitiesof the peaks is such that 175Lu/176Lu = 90/10, then:

�0�974x�/�0�026x + 9�013� = 9 × 174�97/175�90 = 8�95�

Thus x = 108�85�g, which leads to a volume of 0�899/108�85 × 10−6 =82601.

16.3 1. m/e = R2B2/2U , therefore B = �2U�1/2�m/e�1/2/R. For M = 20 massunits, B20 = 0�182T. For M = 200 mass units, B200 = 0�566T. The ratiobetween these two values limiting the field is B200/B20 = 10 = 3�16.

2. If we sweep by a variation in the electric field then there will be, forhigher masses, a voltage ten times weaker resulting in a ten-fold decreasein kinetic energy, lowering the resolving power.

16.4 Intensity of the peak: 720 � I720 = 0�98960 = 0�515.

Intensity of the peak: 721 � I721 = 0�98959 × 0�011 × 60 = 0�344.

The ratio of the two intensities: I721/I720 = 100 × 0�344/0�515 = 66�7%.

16.5 1. Approximate answer: If, following mixing, the peaks 50 and 51 have thesame area and if we accept that the intensity of the signal is proportionalto the mass of the element (and that the intensity reflects the number ofions formed), we would be able to accept that there is 1�g of 51V in 2 gof steel, namely 0�5�g/1g. The mass concentration is therefore 0.5 ppm.

2. More accurate answer:

�51 V/50 V�mass = �50�944/49�947��51 V/50 V�int = 1�02�1/1� = 1�02

If we call x the quantity of V to be found in 2 g of steel:

�51 V/50 V�mass = 1�02 = �0�9975x�/�0�0025x + 1�

we find x = 1�025�g, or 0.513 ppm.

3. If Ti or Cr were present in the steel, there would be a peak of nominalmass 51 due to Cr while the intensity indicating a mass of 50 would bedisturbed by the presence of the Ti.

SOLUTIONS 549

16.6 1. Calculation of the % mass of each of the two isotopes of copper:

%63Cu = 82908 × 62�9296

82908 × 62�9296 + 37 092 × 64�9278× 100 = 68�42

%65Cu = 37 092 × 64�9278

82908 × 62�9296 + 37 092 × 64�9278× 100 = 31�58

Note: On the recording of the mass spectra the areas of the peaksare proportional to the population of the corresponding ions. For theisotopes of an element which do not have the same mass, the % masseswill be a little different.

2. We have added 250�L of a solution of 65Cu at 16 mg/l, therefore

0�25 × 16/1000 = 4 × 10−3 mg or 4mg of 65 Cu�

Following the addition we must calculate, as above, the new % massesof the two isotopes of copper:

% 63Cu = 31775 × 62�9296

31775 × 62�9296 + 79325 × 64�9278× 100 = 27�97

% 65Cu = 79325 × 64�9278

31775 × 62�9296 + 79325 × 64�9278× 100 = 72�03

If we call x the mass of the copper in the sample (x comprises 63Cu and65Cu), we have (in �g):

72�03/27�97 = �0�3158x + 4�/0�6842x

We find x=2�7658�g (in the 250 mg of the original unknown solution tomeasure). Thus for 1 g, there will be 4× 2�7658=11�06�g. This solutioncontains 11.06 ppm of copper.Note: If in place of the two areas we considered the ratio 63Cu/65Cu =2�2352 before adding and 0.4006 following the addition, the calculationswould lead us to the values above.

For example: If y is the % mass in 63Cu:

y/�100 − y� = 2�2352 �62�9296/64�9278� = 2�16641

leading to y = 68�42% and 31.58% of 65Cu.

550 SOLUTIONS

16.7 1. The precise mass corresponding to the molecular formula C15H12O calcu-lated with the more abundant isotopic masses present is as follows:

15 × 12�0000 + 12 × 1�007825 + 1 × 15�994915 = 208�088815u�

The peak M + 1 comprises the sum of the three least abundant isotopicspecies:

a) 12C1413C 1H12

16O

b) 12C151H11

2H 16O

c) 12C151H12

17O

2. The two modes of decomposition correspond to a loss of 28 u. Theions formed (m/z = 180), follow the general rule for radical cations oftype CHO.

3. By the loss of CO: m/z = 208�08822 − �12�000 + 15�99492� = 180�0939.By the loss of C2H4� m/z=208�08822− �24�0000+4�0313�=180�05732.

Following examination of the position of the peaks we can concludethat the more upright peak corresponds to the ions formed when theparent ion loses CO. The molecular formula of this ions is thereforeC14H12, while the second peak has the molecular formula C13H8O.

4. The resolving power is defined by R = M/�M . In considering the scaleof the spectrum, �M at the mid-height of the largest peak (FWHM)corresponds to approximately 0.012 u, leading to R = 15000.

In calculating the exact masses of the three isotopomers of the peakM + 1 (molecular formulae given in Part One), a = 209�09217� b =209�095054 and c=209�09321u. The differences between these values arevery much smaller than the value of �M calculated from the spectrum.Under the conditions of recording the spectrum these three types ofmolecules would appear superimposed.

16.8 1. For macromolecules which cannot be vaporised, particular modes of ioni-sation are used which are similar to methods of impact (FAB or MALDI).Equally ionisation is attained in solution at atmospheric pressure beforethe sample penetrates the MS (processes of electrospray, thermosprayor ionspray). The number of elementary charges carried vary from one

SOLUTIONS 551

macromolecule to another. Since the apparatus records the ratio m/zit will appear as a series of molecular peaks for the same compound.Following the resolution of the MS we will be able to determine M bycalculation from the two peaks (in species carrying different charges), orfrom the isotopic distribution molecular weight (in species of the samecharge state). The recording allows both types of calculation to be made.

2. a) The ratios m/z of the two principal peaks have values close to 1 224and 1 429. We can express two relations:

m/z1 = 1224 and m/z2 = 1429�

Furthermore, we might suppose that the number of charges, greaterfor the peak to the left, differ by one unit from the peak on theright. Therefore, z1 = z2 + 1. This will lead to three equations forthe three unknowns. We begin by calculating z1, finding z2 = 5�97.Since z must be a whole number we will choose z2 = 6. Following on,m = 6 × 1429 = 8574. The ubiquitin has therefore a molecular massof about 8 574 Da.

b) In this method we will consider an enlargement of the isotopic mass1 429�2 < m/z < 1430. Between two successive peaks, m varies by asingle unit of mass. We have for example m/z = 1428�4 and �m +5�/z= 1428�6. So, 5/z= 0�8 and z= 6�25. If we take the most intensepeak located at m/z = 1428�55, we find M = 8571 Da.

17 Labelling methods

17.1 Calling the specific activity of the marker per g AS, the mass of this markerused in g, mS, the activity per g after recuperation AX and the unknownmass (in g) of penicillin in the sample extracted mX.

mS = 1 × 10−2 g�AS = 75000Bq/g and AX = 10 × 1000/1�5 = 6666�7 Bq/g�

mX = 1 × 10−2 × �75000/6666�7 − 1� = 0�102g

In 1 g there is twice as much penicillin, e.g. 0.204 g or 20.4%.

17.2 Following the convention of the previous exercise:

mS = 3mg� AS = 3100Bq/mg�

AX = 3000/30 = 100Bq/mg

552 SOLUTIONS

where

mX = 3 × �3100 − 100�/100 = 90mg or 9%�

17.3 1. The aqueous sample solution of patulin (M = 154g/mol), contains1�54 × 10−3 g/L of this compound. The concentration is therefore 154 ×10−3/154 = 1 × 10−5 M (or 1.54 ppm).

2. The % absorbance (or inhibition) with respect to tube 1:

— tube 2: 0�47/1�03 = 45�63%

— tube 3: 0�58/1�03 = 56/63%

— tube 4 (sample): 0�50/1�03 = 48�54%

3. The absorbance of tube 1 is greater because there is no analyte introducedinto the tube. All of the antibody sites are occupied by the conjugatedenzyme and the absorbance is, as a result, more intense.

4. The quantity of patulin in tube 2 (2 ml) is 1 × 10−5/1000 = 1 × 10−8

mole, equally 1�54�g or 770�g/L (with log C = 2�8865). In tube 3 themolar quantity of patulin is only half, being 0�5 × 10−8 mole, which is0�77�g or again 385�g/L (with log C = 2�5854).

5. Along the x-axis, x = log C (C being in �g/L), and along the y-axis, the% of inhibition, which will lead to the following expression:

�48�54 − 45�63�/�56�63 − 45�63� = �x − 2�5854�/�2�8865 − 2�5854�

leading to x = 2�6651. The value of C is thus 462�4�g/L. The initialsolution is twice the concentration and contains 0.93 mg/L (930 ppb)patulin.

17.4 1. 35Cl +1 n →36 Cl∗ →36 Ar∗ →36 Ar ��− = 3�1 × 105 years�

37Cl +1 n →38 Cl∗ →38 Ar∗ →38 Ar ��− = 37�3 min�

2. The � emissions of 38Cl are preferred since their half-life is short.Counting over a period of time (several hours) and with the aid ofsoftware we can identify the fraction of this isotope with respect to theradiation constant of the emitter of long half-life (less intense).

3. Atomic absorption, but possible loss of volatile elements during thetreatment of the sample. Fluorescence X would be, essentially, analysisof the surface only.

SOLUTIONS 553

4. KCl and AgCl have 74.551 g and 143.321 g for their respective molarmasses. 2 g of KCl corresponds to 2/74�551 = 0�0268 mole. If AgCl wasrecovered totally, its mass would be 143�321×0�0268=3�845g. However,we recover 3.726 g, representing a mass yield of 97%.

50 mL of a solution of AgNO3�M=203�868g/mol, at 15% correspondsto a mass of 7.5 g of this salt, being 7�5/203�868 = 0�037 mole. Wecalculate that the quantity of the silver ion is 0�037/0�0268 = 1�38 timesthe stoichiometric quantity.

5. The numerical value of the � count for a total recovery of the isotope35Cl is 11 203/0�97 = 11549. The quantity of chlorine in the sample is11203/48600×10=2�38�g,which is2�38/0�51=4�66�g/g (or4.7 ppm).

18 Elemental analysis

18.1 %C = 10�56 × �12/44�/5�28 × 100 = 54�55; %H = 4�32 × �2/18�/5�28 ×100 = 9�09; %O = 36�36%

If the compound has the molecular formula CxHyOz and taking M = 88then since there are no significant MS peaks above 89 then it can be deducedthat: �12x/%C� = �y/%H� = �16z/%O� = M/100; Then x = 4; y = 8; z = 2.

18.2 1. Advantage: the cold vapour device is specific for mercury; Disadvantage:only inorganic mercury is measured.

2. Equation of the line of least squares : signal = 858�33 × conc–0�46�C�ppb� = 0�06.

19 Potentiometric methods

19.1 If we call x the molar concentration of the added NH4Cl, at pH=9� H+=10−9 and OH− = 10−5

As a result: KB = NH4OH/NH3= �x + 10−5��10−5�/�9 × 10−3 − 10−5�.Then x = 1�6 × 10−5 M

19.2 Two solutions whose concentrations in H+ ions are different, being Cint

and Cext, are found in part of the special glass membrane which constitutesthe inner wall.

— Potential across the internal face: Eint = RT/F ln��Cint�

— Potential across the external face: Eext = RT/F ln��Cext�

554 SOLUTIONS

Thus in the chain of potentials between the two limits the contribution ofthe membrane:

�Ememb = 0�059 log��Cext� − 0�059 log��Cint�

Since Cint is constant, and if there are no modifications of other charac-teristics of the electrodes, then �Cext alone will interfere with the potentialof the external face of the membrane. The signal depends upon the pH:0.059 pH in mV.

19.3 If x is the concentration in H+ ions:

CH3COOH�CH3COO− + H+ Ka = 1�8 × 10−5

Ka = x2/�0�85 − x� therefore x = 0�0039 and so H+ = 0�0039M with thepH = 2�4. The degree of dissociation will be �0�0039/0�85� × 100 = 0�46%.

19.4 The reaction is the following:

Ti+++ + Fe+++ → Ti4+ + Fe++

Since we have added 1.5 times the stoichiometric quantity of Fe+++ therewill be no more Ti+++. Thus Ti+++ = 0.

Ti4+ = �20/1000� × 10−3 × 1000/50 = �20/50� × 10−3 = 4 × 10−4 M

Fe++ = 4 × 10−4 M

Fe+++ = 2 × 10−4 M�half of the preceding value�

19.5 Cd++ = 0�01. E = E0 − RT/nF lnRed/Ox or E = E0 − 0�059/n� logRed/Ox

E = −0�403 − �0�059/2� × log�1/0�01� = −0�462V�

19.6 The first measurement made with the sample solution was of thefollowing type:

E1 = E′′ + S log Cx

The second was of the following type:

E2 = E′′ + S log�CxVx + CRVR�/�Vx + VR�

SOLUTIONS 555

The term �CxVx + CRVR�/�Vx + VR� represents the new concentration ofthe compound measured when we add the volume VR of concentration CR

to the volume Vx of concentration Cx. Therefore:

�E = E2 − E1 = S log�CxVx + CRVR�/�Vx + VR�Cx

being:

10�E/S = �CxVx + CRVR�/�Vx + VR�Cx

If we isolate Cx from the second member of the expression above then werefind the formula proposed in the question.

20 Voltametric and coulometric methods

20.1 1. Not quite since approximately 0.5% of the sample is electrolysed.

2. The reproducibility of the phenomenon measured to the level of thedrops requires that the diffusion establishes itself in the solution at rest.Stirring renders the system unstable. However, an electrode which turnsregularly can be used.

3. Often the sample is complex and the method of standards is not repre-sentative of the effect of the matrix for the metallic species or the organicmolecules which can react with the electrodes (reductions for example),producing interference.

20.2 We calculate the ratio of the number of transport of zinc with respect tothe number of migrating or diffusing ions present in the solution:

tZn++ = �2 × 5�5 × 10−8 × 10−3�/DC

DC = �2 × 5�5 × 10−8 × 10−3� + �1 × 7�4 × 10−8 × 2 × 10−3�

+ �1 × 7�9 × 10−8 × 0�1� + �1 × 7�6 × 10−8 × 0�1�

tZn++ =6�98 × 10−3

Thus for each coulomb exchanged, the Zn++ ion will transport 6�98×10−3 Cand the rest through the solution �1 − 6�98 × 10−3� = 0�993C. As a resultim/iD = 7�03 × 10−3 or 0.007. The transport of zinc towards the electrode istherefore controlled by the diffusion.

556 SOLUTIONS

20.3 20 drops (approximately 0.16 g) fall in 80 s. The flow of mercury is therefore:

0�16/80 = 2 × 10−3 g/s�

For a distance three times as high, the flow will be three times as much, i.e.6 × 10−3 g/s. The drops always have the same mass and follow a rhythm of:

�0�16/20�/�2 × 10−3� = 1�33 s�

20.4 By application of the equation of Ilkovic (i in �A):

iD = 607 × 2 × �8�67 × 10−6�1/2 × 22/3 × 41/6 × 1 = 7�15�A�

Note: D is in cm2/s; m in mg/s and C in mmol/L.Different units can be used, such as D in m2/s�m in kg/s and C in

mol/m3, leading to iD expressed in amperes.

20.5 The 1 M solution of KCl ready to use is such that Zn = 1ppm. Ifwe prepare a 1 M solution with crystallised KCl, then we will have74�6 × 5/106 = 3�73 × 10−4 g of zinc in 74.6 g of this salt found in 1 litre(which is approximately 1 kg), of solution 0.37 ppm of zinc. The ready-to-use solution is therefore three times more concentrated in zinc than thatprepared with crystallised KCl.

20.6 The number of moles of Zn in the experiment: 25/1000 × 2 × 10−8 =5 × 10−10 mole. We would like to deposit 3% i.e: 0�03 × 5 × 10−10 = 1�5 ×10−11. It requires therefore 3 × 10−11 moles of electrons, representing acharge of:

Q = 96500 × 3 × 10−11 = 2�895 × 10−6 C

Since Q = it� t = 2�895 × 10−6/1�5 × 10−9 = 1�93 × 103 s which is 32.16 min.

Note: A current of 1.5 nA is practically undetectable. However, if we employstripping voltametry, we will redissolve this quantity of zinc in approxi-mately 1 s, which will then produce a much easier signal to detect:

i = 2�895 × 10−6/1 = 2�895�A�

20.7 Standardising the reactant: following the question, 1 mL of this solventhas a water content of 3/15 ml of KF reagent. In oxalic acid dehydrate(M = 126g/mol), the mass concentration of water is 36/126 = 28�57%.

SOLUTIONS 557

The information given permits the following calculation to find the titre ofthe reactant:

T = 0�2857 × 205 × 1/13 = 4�51mg/mL

Measurement: 10 mL of this solvent neutralizes 10×3/15=2mL of reactant,thus 1.05 g of powdered milk will react with 12 − 2 = 10mL of this samereagent. There are therefore 4�51 × 10 = 45�1mg of water in the sample,which is a concentration of

�45�1/1050� × 100 = 4�3%mass�

20.8 In the coulometric version of KF titration 1 molecule of water requires 2atoms of iodine and 2 electrons. Therefore 2 × 96500 coulombs (C), arerequired for one mole, which is 1�8 × 104 mg of water. 1 C corresponds to1�8 × 104/�2 × 96500� = 0�0933mg of water. This then corresponds to thequantity of water of 1 mL of ether. There are therefore 93 mg of water perlitre. Considering the density of ether (0.78 g/ml), the mass concentrationwill be:

93 × 1/0�78 = 120mg/kg�120ppm�

20.9 Two electrons are required to reduce a zinc ion. The quantity of currentused in the experiment is 15 × 10−6 × 5 × 60 = 4�5 × 10−3 C, which willeffectively reduce:

4�5 × 10−3/�2 × 96500� = 2�33 × 10−8 mole of zincknowing that at the beginning of the experiment there were �20/1000� ×1 × 10−3 = 2 × 10−5 mole of zinc. The impoverishment is therefore:

�2�33 × 10−8�/�2 × 10−5� × 100 = 0�12%

22 Basic statistical parameters

22.1Chemist Average

value (x)Standarddeviation(s)

� RSD% Conclusion

Chemist A 131.6 1.56 0.3 1.18 Correct and preciseChemist B 131.6 5.37 0.3 4.08 Correct yet impreciseChemist C 135.7 1.33 3.8 0.98 Incorrect yet preciseChemist D 125.3 9.93 6.6 7.93 Incorrect and imprecise

558 SOLUTIONS

22.2 The average value is 650 with s=1�581. For the level of confidence indicated,the value of t = 2�776. We can then calculate:

t�s/�n�1/2 = 1�963

The results determine a range of 650±1�963 in which we have a 95% chanceof finding the true average. There is probably a systematic error in theseexperiments. However, if we fixed a level of confidence of 99% (t =4�6), wewould have s/�n�1/2 = 3�25 and therefore a range of 650 ± 3�25. The valueof 653 would be included in this interval and would thus be considered asa viable result.

22.3 F = �s1/s2�2 = 11�88. For two series of measurements, the frontier value is

5.05. Therefore the precision of the two apparatus is significantly different.

22.4 The value of t calculated (with n=6) for the chemist A (s =1�559) is 0.471.This value is smaller than those presented in the table of t values: 2.57(for 95%), and 4.03 (for 99%). There is probably not a systematic error.However, for chemist C (s = 1�325), we will find t = 4�05, a value whichindicates a high likelihood of a systematic error.

22.5 The value of Q = �24�8 − 24�36�/�24�8 − 24�10� = 0�63 is inferior to thatwhich is found in the table for five measurements and a level of confidenceof 95% (value 0.64). We should therefore not reject the value 24.8. However,if we recalculate following the addition of the two new values indicated, Qremains unchanged but in the table of seven values we have 0.51. The value24.8 is now rejected.

Note: The values of s and of the average in including (s = 0�239 andaverage 24.29), or by rejecting (s =0�095 and average 24.21) these measure-ments are very different. If we take the middle values we have 24.24 (with),and 24.22 (without). In this case the middle seems preferable to the average.

22.6 The pooled standard deviation sp should be calculated, as follows:

s2p = 6 × 0�32 + 6 × 0�22

14 − 2= 0�25492 t = 3

0�2549

√72

14= 22

In the table t = 2�2, therefore the two methods do not produce at the sameresult.

SOLUTIONS 559

22.7 The problem is centred around the comparison of two averages. That for thefirst percentage purity is 99%, while the average value for the four analysesreported is 98.73 with sn−1 = 0�155. The ‘pooled standard deviation’ of thetwo series of values is:

sp = ��4 × 0�082 + 3 × 0�1552�/7�1/2 = 0�118

The value of t based upon (5+4−2) degrees of freedom leads, accordingto the table, to 2.365 for a level of confidence of 95%.

We must next calculate 2�365 × 0�118 × ��4 + 5�/�4 × 5��1/2 = 0�187 andcompare this value with the difference in the averages of the two series,99 − 98�73 = 0�23. The result of this comparison appears rather large andtherefore leads to the conclusion that the two averages can be consideredto be incompatible. Thus the original value will not be retained.

22.8 If we consider that the law of variation of the absorbance with the concen-tration is a straight line then this will have the equation: A = 0�05 conc +0�08. The difference are relatively large. A quadratic adjustment would bepreferred and across a narrower range of concentrations.

22.9 For the blank, sn−1 =0�82. The value of t calculated for 5+ 8 measurementsis 3.17. Therefore �x = 3�17 × 0�82 × �5 + 8�/�5 × 8�1/2 = 1�48. The limitof the detection is around 1.5 mg.

AppendixList of acronyms

AAS Atomic absorption spectroscopyAC Alternative currentADC Analogue–digital converterAED Atomic emission detectorAES Atomic emission spectroscopyAGS Amperometric gas sensorAMS Accelerator mass spectrometryAMTIR Amorphous material transmitting infrared radiationAPCI Atmospheric pressure chemical ionisationAPXS Alpha particle X-ray spectrometerASTM American Society for Testing MaterialsATR Attenuated total reflectanceBSA Bovine serum albuminCCD Charge-coupled deviceCE Capillary electophoresisCEC Capillary electrochromatographyCGE Capillary gel electrophoresisCI Chemical ionizationCID Collision-induced dissociationCIEF Capillary isoelectric focusingCV Coefficient of variationCVAFS Cold vapour atomic fluorescence spectroscopyCZE Capillary zone electrophoresisCW Continuous waveDAD Diode array detector (or detection)DCP Direct current polarographyDPP Differential pulsed polarographyDTGS Deuterated triglycine sulfateECD Electron capture detectorEDL Electrodeless discharge lamp


562 APPENDIX LIST OF ACRONYMS

EDTA Ethylenediamine-tetracetic acidEDXRF Energy dispersive X-ray fluorescenceEI Electron impact (or ionization)EIA Enzymatic immuno-assayELISA Enzyme linked immunosorbent assayEOF Electro-osmotic flowESCA Electron spectroscopy for chemical analysisESI Electrospray ionizationFAB Fast atom bombardmentFES Flame emission spectroscopyFID Flame ionization detectorFID Free induction decayFPD Flame photometry detectorFT Fourier transformFTIR Fourier transform infraredFTMS Fourier transform mass spectrometryFWHM Full width at half maximumGC Gas chromatographyGC-MS Gas chromatography mass spectrometryGC-ICP Gas chromatography–inductively coupled plasmaGDL Glow discharge lampGFC Gel filtration chromatographyGLC Gas liquid chromatographyGLP Good laboratory practiceHPCE High performance capillary electrophoresisHCL Hollow cathode lampHETP Height equivalent to a theoretical plateHIC Hydrophobic interaction chromatographyHOMO Highest occupied molecular orbitalHPLC High performance liquid chromatographyHPTLC High performance thin layer chromatographyHRP Horseradish peroxidaseIC Ion chromatographyICP Inductively coupled plasmaICPMS Inductively coupled plasma mass spectrometryICRMS Ion cyclotron resonance mass spectrometryIEA Immuno-enzymological assayIEC Internal electron captureIFA Immunofluorescence assayIMS Ion mobility spectrometerIR InfraredISE Ionic selective electrodeKK Kramers KrönigLIDAR Light detection and ranging

APPENDIX LIST OF ACRONYMS 563

LOMO Lowest occupied molecular orbitalLPME Liquid phase micro-extractionMALDI Matrix-assisted laser desorption ionizationMCA Multicomponent analysisMCT Mercury cadmium tellurideMEKC Micellar electrokinetic capillary chromatographyMIKE Mass ion kinetic energyMLRA Multiwavelength linear regression analysisMRI Magnetic resonance imagingMS Mass spectrometryMS-MS Tandem mass spectrometryMSD Mass spectrometer detectorNAA Neutron activation analysisNADH Nicotinamide adenine dinucleotide reduced formNIR Near infraredNMR Nuclear magnetic resonanceNPD Nitrogen phosphorous detectorNPP Normal pulsed polarographyOES Optical emission spectrometryOFAT One-factor-at-a-timePAGE Polyacrylamide gel electrophoresisPAH Polynuclear aromatic hydrocarbonsPCA Principal component analysisPDA Photodiode arrayPID Photo ionization detctorPLS Partial least squarePMT Photo multiplier tubePOPOP 1,4-Bis(5-phenyloxazo1-2-yl)benzeneppb parts per billionppm parts per millionPPO 2,5-diphenyloxazoleppt parts per trillionPT Peak tailingPTV Programmed temperature vaporizationRIA Radio-immunoassayRP Reversed phaseRSD Relative standard deviationSCE Standard calomel electrodeSEC Size exclusion chromatographySFC Supercritical fluid chromatographySFE Supercritical fluid extractionSEM Scanning electron microscopeSPE Solid-phase extractionSPME Solid-phase micro-extraction

564 APPENDIX LIST OF ACRONYMS

SV Stripping polarographyTCD Thermal conductivity detectorTI Thermal ionizationTIC Total ion chromatogramTISAB Total ionic strength adjustment bufferTLC Thin layer chromatographyTMS TetramethylsilaneTOF Time of flightTZ Trennzahl numberUV UltravioletVOC Volatile organic compoundWCOT Wall coated open tubularWXRF Wavelength dispersive X-ray fluorescence

Bibliography

Baker, D.R. (1995) Capillary Electrophoresis, John Wiley, ISBN 0-471-11763-3.Broekaert, J.A.C. (2005) Analytical Atomic Spectrometry With Flames And Plasmas

(2nd edn), John Wiley & Sons Inc, ASIN : 352731282X.Christian, G.D. (2003) Analytical Chemistry (6th Int. edn), John Wiley, ISBN 0-471-

451622.Crosby, N.T., Davy, J.A., Hardcastle, W.A., Holcombe, D.G. and Treble, R.D.

(1995) Quality in the Analytical Chemistry Laboratory, ACOL series, ISBN0-471-95470-5.

De Hoffmann, E., Charette, J, and Stroobant, V. (1996) Mass Spectrometry: Principlesand Applications, John Wiley, ISBN 0-471-96697-5.

Deportes, C. (1994) Electrochimie des Solides, Presses Universitaires de Grenoble,ISBN 2-7061-0585-2.

Fried, B. and Sherma, J. (1996) Practical Thin-Layer Chromatography, Springer-Verlag, ISBN 0-8493-2660-5.

George, W.O. and McIntyre, P.S. (1987) Infrared Spectroscopy, John Wiley, ISBN0-471-91389-9.

Gunther, H., Suffert, J.-J, and Ourisson. G. (1994) La Spectroscopie de RMN, Masson,ISBN 2–225-84029-6.

Harris D.C. (2004) Exploring Chemical Analysis (3rd edn) W H Freeman & Co (Sd)ASIN 0716705710.

Higson S.P.J. (2003) Analytical Chemistry Oxford Univ Pr (Sd), ISBN 0-198-50289-3.Kellner, R., Mermet J.M., Otto, M., and Widmer H.M. (1998) Analytical Chemistry,

Wiley-VCH ISBN 3-527-28881-3.Maurice, J. (1993) Jugement Statistique sur Echantillons en Chimie, Polytechnica,

ISBN 2-84054-013-4.Miller, J.N. and Miller. J.C. (2005) Statistics & Chemometrics for Analytical Chemistry

(5th edn), Prentice Hall Ptr ISBN 0-13-1291920.Murray, R. (1992) Instrumentation in Analytical Chemistry, Louise Voress, ISBN

0-8412-2202-9.Rosset, R., Caude, M. and Jardy, A. (1991) Chromatographie en Phase Liquide et

Supercritique, Masson, ISBN 2-225-82308-1.Sandra, P. (1989) High Resolution Gas Chromatography (3rd edn), in Hyver, K.J.

(ed.), Hewlett-Packard Co, ISSN 5950-3562.Skoog, D.A., West, D.M., Holler, F.J. and Crouch, S.R. (2004) Fundamen-

tals of Analytical Chemistry (8th edn), Saunders College Publishing, ISBN0-03-005938-0.


566 BIBLIOGRAPHY

Smith, M. and Busch, K.L. (1999) Understanding Mass Spectra: A Basic Approach,John Wiley, ISBN 0-471-29704-6.

Techniques de l’ingénieur (various years) Analyse Chimique et Caracterisation, Vol.Pl, P2, P3, P4, Istra, ISSN 0245-9639.

Tranchant, J. (1994) Manuel Pratique de Chromatographie en Phase Gazeuse, Masson,ISBN 2-225-84681-2.

Table of some useful constants

Physical constants

Quantity Symbol Value Units

Speed of light in vacuum c 2.9979 × 108 m/sVacuum permittivity �0 8.8542 × 10–12 F/mVacuum permeability �0 4� × 10–7 H/mElementary charge e 1.6022 × 10–19 CElectron rest mass me 9.1094 × 10–31 kgProton rest mass mp 1.6726 × 10–27 kgNeutron rest mass mn 1.6750 × 10–27 kgAtomic mass constant u 1.6605 × 10–27 kgPlanck’s constant h 6.6261 × 10–34 J sDirac constant � = h/2� 1.0546 × 10–34 J sAvogadro number NA 6.0221 × 1023 /molFaraday constant F = NAe 9.6485 × 104 C/molBoltzmann constant k = R/NA 1.3807 × 10–23 J/KMolar gas constant R = NAkB 8.3145 J/K molGravitational constant G 6.6720 × 10–11 N m2/kg2

Unit conversion1 Å = 10–10 m 1 cm–1 = 2.9979 × 1010 Hzl eV = 1.6022 × 10–19 J 1 atm = 1.0133 × 105 Pa; 1 bar = 105 Pa

Prefixes

Symbol f p n � m c d k MName femto pico nano micro milli centi deci kilo megaFactor 10–15 10–12 10–9 10–6 10–3 10–2 10–1 103 106


Index

AB system (NMR) 351Absolute experimental error 502Absolute response factor 105, 107Absorbance 82, 167, 169, 178, 181,

182, 187, 208Absorption coefficient 187Absorption filter 277Adjusted retention time 7, 13, 14Adsorption coefficient 24, 27, 73AED 50AES 309AGS 474Alkaline error 457AMS 409AMTIR 225Anionic column 94Anionic exchange resin 102Antibody 426Antigen 425APCI 399APXS 270ATR 227Auger electron 264Auxiliary electrode 465

Back-pressure regulator 130Bandwidth 189, 287, 322, 323Bathochromic effect 174, 176Beam-splitter 217Biosensor 476Bleeding 26Bloch theory 331Blue shift 175

Bragg relationship 274Bremsstrahlung 267Burner (AAS) 291

Capacitive current 469Capacity factor 15Capillary Column 39Carrier gas 31Cationic column 94Cell thickness 235Charge transfer spectra 169Chemical ionization 393Chemical shift 340Chemical vaporization 296Chemifluorescence 253Chemiluminescence 256, 445Chiral stationary phase 43, 75Chromatogram 5Chromogene 173Chromophore 173CIEF 157Clark probe 473Coating efficiency 22Coefficient of variation 504Cold on-column injection 37Colorimeter, infrared 221Colorimetry 191Compression factor 34Conductivity 100Confidence interval 506Confirmatory analysis 192Cooley algorithm 218Coomassie blue 147


570 INDEX

Correlation coefficient 512Coulombic force 374Coulometric titration 480Counter electrode 465Coupling constant 346Critical pressure 127Critical temperature 127Cyclodextrin 43, 75

Dead time 7Dead volume 15Deconvolution 196Dense gas 130Densitometer 123Depolarizer 465Derivative graph 200Deshielding, NMR 340Detector, MCT 224Detector, PbS 224Determination coefficient 513Deuterium arc lamp 298Diffuse reflection 230Diffusion coefficient 136,

137Diffusion current 468Dispersive spectrometer 216Distribution coefficient 16Dixon’s test 510DOE 515Double-beam spectrometer 183

ECD 48Echelle grating 318Eddy diffusion 20EDL 293EDTA 304EDXRF 273Effective cross-section 435Efficiency 12EIA 426Electro-migration injection 153Electrochromatography 159Electrodeless discharge lamp 293Electrolyte buffer 145

Electronic energy 169Electronic transition 171–3Electropherogram 148Electrophoretic mobility 149Electrospray 398ELISA 425Elution 7Elution gradient 67Elution time 22Enantiomeric excess 76Equivalent height 14ESCA 265Experimental error 502, 503External reference electrode 453External standard 105

Factor J 34far infrared 207Far UV 171Faraday diffusion 470Fast atom bombardment 394Fast chromatography 52FID (NMR) 338, 361FID Detector 47Fluorescence 185, 241Fluorescence ratio 250Fluorophore 253Force constant 210Fourier transform spectrometer 216,

220Fragmentation spectrum 371Free induction decay 338Free solution electrophoresis 155FTIR 217

Gel filtration 135, 137Gel permeation 135GFC 135Glass electrode 455Glow discharge 315Glucose oxidase 477Golay’s equation 21GPC 135Gram-Schmidt 232

INDEX 571

Guard column 70Gyromagnetic constant 329

Half-life 423Hapten 426Harmonic oscillator 210HCL 292, 301Headspace 494Heteronuclear coupling 345HETP 9High speed chromatography 52Hold-up time 7, 13, 14Hold-up volume 15Hollow cathode lamp 292Holmium oxide 184Homonuclear coupling 345Horseradish peroxidase 427, 428Hydrophobic interaction chrom. 80Hydrophobic phase 77Hydrostatic injection 153Hyperchromic effect 174Hypsochromic effect 175

ICP 311ICRMS 387IFA 431Immersion probe 186Immunoaffinity extraction 490IMS 380Index of hydrogen deficiency 405Indirect UV detection 155Inductively coupled plasma 311Inert binder 117, 457Infrared detector 51Injection loop 105, 153Injection peak 99Insert 35Internal conversion 243Internal normalization 110Internal reference electrode 453Internal standard 107Internal standard method (NMR) 358Ion filter 383Ion mobility spectrometer 380

Ion pairing agent 78Ion selective electrode 453, 454Ion trap 385Ionophore 458Ionspray 398Isobestic point 190Isocratic mode 66Isotope labelling 431Isotopic abundances 406Isotopic ratios 409

JCAMP-DX 232

Karl Fischer reagent 481, 482Kirchhoff 285Kjeldahl nitrogen 445Knox’s equation 22Kovat’s retention index 54

Labelling method 419Lambda sensor 463Lambert-Beer law 186–189, 192, 199,

247, 278, 290Larmor frequency 333Least square regression 512Library, spectral 404LIDAR 249Lifetime 242, 255Light scattering 196, 201Limiting migration velocity 148Linear attenuation coefficient 278Linear dispersion 322Liquid membrane electrode 458Longitudinal relaxation 339Lorentz force law 374Luminol 257, , 260

McLafferty 411Magic angle 331, 365Magnetization 333Magnetogyric constant 329Make-up gas 49MALDI 395Mass flow 47Mass spectrum 370, 372

572 INDEX

Mass to charge ratio 369Matrix 487Maxwell-Boltzmann 287Mc Reynolds’ constant 57Mean deviation 504Mean value 501MEKC 155Merryfield’s resin 97Metastable ion peak 413Micro-column 87Microbore 69Microchannel plate detector 402Microwave digester 498mid infrared 207Mineralization 498MLRA 194MLS 196Monochromatic detection 82Monolithic column 88Monomeric phase 73Morton and Stubbs 197MRI 353MSD 50Multicharged ions 398, 399, 407

Narrow bore 69Natural bandwidth 287near infrared 167, 211Near- IR 167Near UV 167Nebulizer 294, 313, 314Nephelometry 192Nernst source 221Neutral marker 150Neutron activation 432Neutron capture 433Ninhydrin 119Normal mass spectrum 371Normal phase 76NPD 48Nuclear magnetic moment 329Nujol 226Null hypothesis 508

OES 309One factor at a time 515Optical density 169Optical purity 76Orthosilicic acid 71

Packed capillary 66Packed column 41, 87PAGE 155Partition coefficient 11, 26Pascal’s triangle 348PCR 196Peak matching 378, 414Phase ratio 44Phosphorescence 241Photoelectric effect 264Photoionisation 264Photomultiplier tube 181, 182PID 50Plate theory 9Plot 41, 44PLS 196Polarogram 467–8Polychromatic detection 82Polychromator 317Polymeric phase 74Polysiloxanes 43POPOP 424Potentiostatic coulometry 480PPO 424Precolumn 70Proportional counter 271PTV 38Pulsed wave NMR 338Purge and trap 494Pyroelectric detector 222

Quadrupole analyzer 381, 383, 384Quantum yield 245, 246Quenching 245

Radical cation 410Radio-immunology 422Radioactive decay constant 423Radiocarbon 424

INDEX 573

Radionuclide 423Raman diffusion 247Rate theory 19Rayleigh scattering 247, 265Red shift 176Reference electrode 465Refractive index detector 140Relative error 503Relative response factor 107,

108, 110Resin film 98Resolution factor 17, 22Resolving power 321, 389Retention factor 15Retention index 54Retention time 5, 11, 14Retention time locking 57Retention volume 15Reversed phase 73, 76Reversed polarity 118Rf 124Robust statistics 508RP-HPLC 73Ruhemann purple 146

Saturation factor 436Scintillator 424Screening effect 342Selectivity 95SEM 271Separation factor 17Septum 35Sequential spectrometer 178, 317Shielding, NMR 340Siegbahn 266Silanol group 71Silica gel 71Simultaneous spectrometer 178Single beam spectrometer 182Skewing factor 8Slope factor 460Smith-Hieftje 301Solid phase extraction 96Solvatochromism 174

Spark ionization 314SPE 488Speciation analysis 288Specific activity 420Specific conductance 101Spectral libraries 233Spectral line width 315–17Spectrum, NMR 328Specular reflection 228Spin 328Spin decoupling 352Spin number 331Split cold injection 38Split/splitless injection 35, 38Standard addition method 461Standard deviation 504Stationary phase constant 54Stokes shift 243Substoichiometric 421Supercritical fluid 127Suppressor 99, 101Syringe pump 130

Tandem mass spectrometer401

Tast polarography 469TC 447, 448TCD 46Theoretical plate 9Thermal ionization 397Thermal neutrons 434Thermoelectric atomization 295Thomson 371TIC 448TMS 341TOC 448TOF analyzer 379Total carbon 447Total ionic current 50Total systematic error 502Transmittance 169, 208Transverse relaxation 339Trennzahl number 56True mean 504

574 INDEX

True value 502Two dimensional TLC 120

Van Deemter 19, 33, 131Vibrational relaxation 244Visual colorimetry 202Void volume 135Voltammogram 466

Water dip 99Wavelength calibration 184Wavenumber 208WCOT 41WDXRF 273Working electrode 453

Zeeman effect 300

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